From e8a0b68a618fb378aaa2703ea060663e65a511aa Mon Sep 17 00:00:00 2001
From: Lei Fang <LFlvb@users.noreply.github.com>
Date: Thu, 16 Jun 2016 19:27:29 +0200
Subject: [PATCH 01/63] Add files via upload

---
 MuPoMo_bootstrap/Histogram of theta1.png        | Bin 0 -> 57049 bytes
 ...Prediction intervals at different levels.png | Bin 0 -> 69546 bytes
 2 files changed, 0 insertions(+), 0 deletions(-)
 create mode 100644 MuPoMo_bootstrap/Histogram of theta1.png
 create mode 100644 MuPoMo_bootstrap/Prediction intervals at different levels.png

diff --git a/MuPoMo_bootstrap/Histogram of theta1.png b/MuPoMo_bootstrap/Histogram of theta1.png
new file mode 100644
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From bd54d3a55ded869b8c18c4c767beb86cdf122ffa Mon Sep 17 00:00:00 2001
From: Lei Fang <LFlvb@users.noreply.github.com>
Date: Thu, 16 Jun 2016 19:28:00 +0200
Subject: [PATCH 02/63] Delete Histogram of theta1.pdf

---
 MuPoMo_bootstrap/Histogram of theta1.pdf | Bin 4663 -> 0 bytes
 1 file changed, 0 insertions(+), 0 deletions(-)
 delete mode 100644 MuPoMo_bootstrap/Histogram of theta1.pdf

diff --git a/MuPoMo_bootstrap/Histogram of theta1.pdf b/MuPoMo_bootstrap/Histogram of theta1.pdf
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From fc71399e21add8c23c31a6bf53371d5f2afdffc6 Mon Sep 17 00:00:00 2001
From: Lei Fang <LFlvb@users.noreply.github.com>
Date: Thu, 16 Jun 2016 19:28:18 +0200
Subject: [PATCH 03/63] Delete Prediction intervals at different levels.pdf

---
 .../Prediction intervals at different levels.pdf | Bin 8138 -> 0 bytes
 1 file changed, 0 insertions(+), 0 deletions(-)
 delete mode 100644 MuPoMo_bootstrap/Prediction intervals at different levels.pdf

diff --git a/MuPoMo_bootstrap/Prediction intervals at different levels.pdf b/MuPoMo_bootstrap/Prediction intervals at different levels.pdf
deleted file mode 100644
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From 5b4eb2fd1b3326c517bf7cf9e392343eee7159c1 Mon Sep 17 00:00:00 2001
From: Lei Fang <LFlvb@users.noreply.github.com>
Date: Thu, 16 Jun 2016 19:29:22 +0200
Subject: [PATCH 04/63] Add files via upload

---
 .../Multi-Population model with German data.png | Bin 0 -> 75408 bytes
 ...ulti-Population model with Japanese data.png | Bin 0 -> 87504 bytes
 2 files changed, 0 insertions(+), 0 deletions(-)
 create mode 100644 MuPoMo_main_multipop/Multi-Population model with German data.png
 create mode 100644 MuPoMo_main_multipop/Multi-Population model with Japanese data.png

diff --git a/MuPoMo_main_multipop/Multi-Population model with German data.png b/MuPoMo_main_multipop/Multi-Population model with German data.png
new file mode 100644
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From cf00d98f99ae3df25bc80e9701e352e097a2c780 Mon Sep 17 00:00:00 2001
From: Lei Fang <LFlvb@users.noreply.github.com>
Date: Thu, 16 Jun 2016 19:29:46 +0200
Subject: [PATCH 05/63] Delete Multi-Population model with German data.pdf

---
 .../Multi-Population model with German data.pdf  | Bin 7878 -> 0 bytes
 1 file changed, 0 insertions(+), 0 deletions(-)
 delete mode 100644 MuPoMo_main_multipop/Multi-Population model with German data.pdf

diff --git a/MuPoMo_main_multipop/Multi-Population model with German data.pdf b/MuPoMo_main_multipop/Multi-Population model with German data.pdf
deleted file mode 100644
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From 1a80b14d950ce3fa93f74d2d080ee52c17696933 Mon Sep 17 00:00:00 2001
From: Lei Fang <LFlvb@users.noreply.github.com>
Date: Thu, 16 Jun 2016 19:30:01 +0200
Subject: [PATCH 06/63] Delete Multi-Population model with Japanese data.pdf

---
 ...Multi-Population model with Japanese data.pdf | Bin 8796 -> 0 bytes
 1 file changed, 0 insertions(+), 0 deletions(-)
 delete mode 100644 MuPoMo_main_multipop/Multi-Population model with Japanese data.pdf

diff --git a/MuPoMo_main_multipop/Multi-Population model with Japanese data.pdf b/MuPoMo_main_multipop/Multi-Population model with Japanese data.pdf
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From b92f5c29f498bf8237e0e47a18091bc05b13800a Mon Sep 17 00:00:00 2001
From: Lei Fang <LFlvb@users.noreply.github.com>
Date: Thu, 16 Jun 2016 19:31:10 +0200
Subject: [PATCH 07/63] Add files via upload

---
 .../Contour plot of theta2 and theta4.png      | Bin 0 -> 380185 bytes
 MuPoMo_main_twopop/Loss function of theta2.png | Bin 0 -> 74869 bytes
 MuPoMo_main_twopop/Model fit and forecast.png  | Bin 0 -> 87878 bytes
 .../Time shift at different levels.png         | Bin 0 -> 92248 bytes
 4 files changed, 0 insertions(+), 0 deletions(-)
 create mode 100644 MuPoMo_main_twopop/Contour plot of theta2 and theta4.png
 create mode 100644 MuPoMo_main_twopop/Loss function of theta2.png
 create mode 100644 MuPoMo_main_twopop/Model fit and forecast.png
 create mode 100644 MuPoMo_main_twopop/Time shift at different levels.png

diff --git a/MuPoMo_main_twopop/Contour plot of theta2 and theta4.png b/MuPoMo_main_twopop/Contour plot of theta2 and theta4.png
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diff --git a/MuPoMo_main_twopop/Model fit and forecast.png b/MuPoMo_main_twopop/Model fit and forecast.png
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From 532c26e0a79b1347c7ebc60a35305555e6ef2911 Mon Sep 17 00:00:00 2001
From: Lei Fang <LFlvb@users.noreply.github.com>
Date: Thu, 16 Jun 2016 19:31:38 +0200
Subject: [PATCH 08/63] Delete Contour plot of theta2 and theta4.pdf

---
 .../Contour plot of theta2 and theta4.pdf       | Bin 35972 -> 0 bytes
 1 file changed, 0 insertions(+), 0 deletions(-)
 delete mode 100644 MuPoMo_main_twopop/Contour plot of theta2 and theta4.pdf

diff --git a/MuPoMo_main_twopop/Contour plot of theta2 and theta4.pdf b/MuPoMo_main_twopop/Contour plot of theta2 and theta4.pdf
deleted file mode 100644
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From 1146016fffad7e06f4d1452f75d757935b5e2b9f Mon Sep 17 00:00:00 2001
From: Lei Fang <LFlvb@users.noreply.github.com>
Date: Thu, 16 Jun 2016 19:32:03 +0200
Subject: [PATCH 09/63] Delete Loss function of theta2.pdf

---
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 1 file changed, 0 insertions(+), 0 deletions(-)
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diff --git a/MuPoMo_main_twopop/Loss function of theta2.pdf b/MuPoMo_main_twopop/Loss function of theta2.pdf
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From 0630b6c309a423d0332d732344904f4cb4467e25 Mon Sep 17 00:00:00 2001
From: Lei Fang <LFlvb@users.noreply.github.com>
Date: Thu, 16 Jun 2016 19:32:21 +0200
Subject: [PATCH 10/63] Delete Model fit and forecast.pdf

---
 MuPoMo_main_twopop/Model fit and forecast.pdf | Bin 10704 -> 0 bytes
 1 file changed, 0 insertions(+), 0 deletions(-)
 delete mode 100644 MuPoMo_main_twopop/Model fit and forecast.pdf

diff --git a/MuPoMo_main_twopop/Model fit and forecast.pdf b/MuPoMo_main_twopop/Model fit and forecast.pdf
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From b745cb56c6e2d4a8bdae39898b50a85e4a26d2fe Mon Sep 17 00:00:00 2001
From: Lei Fang <LFlvb@users.noreply.github.com>
Date: Thu, 16 Jun 2016 19:32:35 +0200
Subject: [PATCH 11/63] Delete Time shift at different levels.pdf

---
 .../Time shift at different levels.pdf           | Bin 6116 -> 0 bytes
 1 file changed, 0 insertions(+), 0 deletions(-)
 delete mode 100644 MuPoMo_main_twopop/Time shift at different levels.pdf

diff --git a/MuPoMo_main_twopop/Time shift at different levels.pdf b/MuPoMo_main_twopop/Time shift at different levels.pdf
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From 5af75d41a3714805b749c7c8a95f35d50957bd84 Mon Sep 17 00:00:00 2001
From: Lukas Borke <admin@quantnet.technology>
Date: Fri, 17 Jun 2016 12:27:58 +0200
Subject: [PATCH 12/63] Update Metainfo.txt

---
 MuPoMo_bootstrap/Metainfo.txt | 3 +--
 1 file changed, 1 insertion(+), 2 deletions(-)

diff --git a/MuPoMo_bootstrap/Metainfo.txt b/MuPoMo_bootstrap/Metainfo.txt
index e888743..97468f3 100644
--- a/MuPoMo_bootstrap/Metainfo.txt
+++ b/MuPoMo_bootstrap/Metainfo.txt
@@ -2,8 +2,7 @@ Name of QuantLet :  MuPoMo_bootstrap
 
 Published in :      MuPoMo
 
-Description :      ‘Forecasts mortality rates based on a semi-parametric approach, and bootstraps time series with innovation to compute
-                    the prediction intervals. Uses random two countries to demonstrate.’
+Description :      'Forecasts mortality rates based on a semi-parametric approach, and bootstraps time series with innovation to compute the prediction intervals. Uses random two countries to demonstrate.'
 
 Keywords :         ‘time series, demography, mortality, population, nonparametric smoothing, parametric modelling, Lee-Carter method,
                     bootstrap’

From 4353812cbe1539b0a941eac11fb4c76105cf4352 Mon Sep 17 00:00:00 2001
From: Lei Fang <LFlvb@users.noreply.github.com>
Date: Fri, 17 Jun 2016 13:44:03 +0200
Subject: [PATCH 13/63] Update Metainfo.txt

---
 MuPoMo_bootstrap/Metainfo.txt | 8 ++++----
 1 file changed, 4 insertions(+), 4 deletions(-)

diff --git a/MuPoMo_bootstrap/Metainfo.txt b/MuPoMo_bootstrap/Metainfo.txt
index 97468f3..42fb734 100644
--- a/MuPoMo_bootstrap/Metainfo.txt
+++ b/MuPoMo_bootstrap/Metainfo.txt
@@ -4,11 +4,11 @@ Published in :      MuPoMo
 
 Description :      'Forecasts mortality rates based on a semi-parametric approach, and bootstraps time series with innovation to compute the prediction intervals. Uses random two countries to demonstrate.'
 
-Keywords :         ‘time series, demography, mortality, population, nonparametric smoothing, parametric modelling, Lee-Carter method,
-                    bootstrap’
+Keywords :         'time series, demography, mortality, population, nonparametric smoothing, parametric modelling, Lee-Carter method,
+                    bootstrap'
 
-See also :         ‘MuPoMo_data, MuPoMo_optimization, MuPoMo_normalization, 
-                    MuPoMo_referencecurve, MuPoMo_main_twopop, MuPoMo_main_multipop’
+See also :         'MuPoMo_data, MuPoMo_optimization, MuPoMo_normalization, 
+                    MuPoMo_referencecurve, MuPoMo_main_twopop, MuPoMo_main_multipop'
 
 Author :            Lei Fang
 

From 0bca2d71b1d5e72789f81dc0189ad59df6e9606a Mon Sep 17 00:00:00 2001
From: Lei Fang <LFlvb@users.noreply.github.com>
Date: Fri, 17 Jun 2016 13:45:41 +0200
Subject: [PATCH 14/63] Update Metainfo.txt

---
 MuPoMo_data/Metainfo.txt | 8 ++++----
 1 file changed, 4 insertions(+), 4 deletions(-)

diff --git a/MuPoMo_data/Metainfo.txt b/MuPoMo_data/Metainfo.txt
index 0b6efd1..c9e4bdb 100644
--- a/MuPoMo_data/Metainfo.txt
+++ b/MuPoMo_data/Metainfo.txt
@@ -3,12 +3,12 @@ Name of QuantLet :  MuPoMo_data
 Published in :      MuPoMo
 
 Description :      'Reads data from Human Mortality Database and calculate kt, and will be called
-                    in MuPoMo_main_twopop and MuPoMo_main_multipop.’
+                    in MuPoMo_main_twopop and MuPoMo_main_multipop.'
 
-Keywords :         ‘time series, demography, mortality, Lee-Carter method, population, Human Mortality Database’
+Keywords :         'time series, demography, mortality, Lee-Carter method, population, Human Mortality Database'
 
-See also :         ‘MuPoMo_optimization, MuPoMo_normalization, MuPoMo_referencecurve, 
-                    MuPoMo_main_twopop, MuPoMo_main_multipop, MuPoMo_bootstrap’
+See also :         'MuPoMo_optimization, MuPoMo_normalization, MuPoMo_referencecurve, 
+                    MuPoMo_main_twopop, MuPoMo_main_multipop, MuPoMo_bootstrap'
 
 Author :            Lei Fang
 

From ac6c84c24754869fe7789467550050a4af9f17c7 Mon Sep 17 00:00:00 2001
From: Lei Fang <LFlvb@users.noreply.github.com>
Date: Fri, 17 Jun 2016 13:46:35 +0200
Subject: [PATCH 15/63] Update Metainfo.txt

---
 MuPoMo_main_multipop/Metainfo.txt | 8 ++++----
 1 file changed, 4 insertions(+), 4 deletions(-)

diff --git a/MuPoMo_main_multipop/Metainfo.txt b/MuPoMo_main_multipop/Metainfo.txt
index 6b94f6d..d282fce 100644
--- a/MuPoMo_main_multipop/Metainfo.txt
+++ b/MuPoMo_main_multipop/Metainfo.txt
@@ -3,12 +3,12 @@ Name of QuantLet :  MuPoMo_main_multipop
 Published in :      MuPoMo
 
 Description :      'Estimates and forecasts mortality rates based on a semi-parametric approach, which applies parametric modelling for 
-                    multiple nonparametric smoothed curves with the shape-related nonlinear variation.’
+                    multiple nonparametric smoothed curves with the shape-related nonlinear variation.'
 
-Keywords :         ‘time series, demography, mortality, population, nonparametric smoothing, parametric modelling, Lee-Carter method’
+Keywords :         'time series, demography, mortality, population, nonparametric smoothing, parametric modelling, Lee-Carter method'
 
-See also :         ‘MuPoMo_data, MuPoMo_optimization, MuPoMo_normalization, 
-                    MuPoMo_referencecurve, MuPoMo_main_twopop, MuPoMo_bootstrap’
+See also :         'MuPoMo_data, MuPoMo_optimization, MuPoMo_normalization, 
+                    MuPoMo_referencecurve, MuPoMo_main_twopop, MuPoMo_bootstrap'
 
 Author :            Lei Fang
 

From 7988f38ced40798440b335cf2c5acea39bbafeb2 Mon Sep 17 00:00:00 2001
From: Lei Fang <LFlvb@users.noreply.github.com>
Date: Fri, 17 Jun 2016 13:47:35 +0200
Subject: [PATCH 16/63] Update Metainfo.txt

---
 MuPoMo_main_twopop/Metainfo.txt | 10 +++++-----
 1 file changed, 5 insertions(+), 5 deletions(-)

diff --git a/MuPoMo_main_twopop/Metainfo.txt b/MuPoMo_main_twopop/Metainfo.txt
index 09b2ce3..8a599d9 100644
--- a/MuPoMo_main_twopop/Metainfo.txt
+++ b/MuPoMo_main_twopop/Metainfo.txt
@@ -4,13 +4,13 @@ Published in :      MuPoMo
 
 Description :      'Estimates and forecasts mortality rates based on a semi-parametric approach, which applies parametric modelling for 
                     multiple nonparametric curves with the shape-related nonlinear variation. Uses random two countries to demonstrate 
-                    two-country case.’
+                    two-country case.'
 
-Keywords :         ‘time series, demography, mortality, population, nonparametric smoothing, parametric modelling, Lee-Carter method,
-                    contour’
+Keywords :         'time series, demography, mortality, population, nonparametric smoothing, parametric modelling, Lee-Carter method,
+                    contour'
 
-See also :         ‘MuPoMo_data, MuPoMo_optimization, MuPoMo_normalization, 
-                    MuPoMo_referencecurve, MuPoMo_main_multipop, MuPoMo_bootstrap’
+See also :         'MuPoMo_data, MuPoMo_optimization, MuPoMo_normalization, 
+                    MuPoMo_referencecurve, MuPoMo_main_multipop, MuPoMo_bootstrap'
 
 Author :            Lei Fang
 

From e6317d9de9fa7fb0e9e86764ca5f75fa68da1ebc Mon Sep 17 00:00:00 2001
From: Lei Fang <LFlvb@users.noreply.github.com>
Date: Fri, 17 Jun 2016 13:48:12 +0200
Subject: [PATCH 17/63] Update Metainfo.txt

---
 MuPoMo_normalization/Metainfo.txt | 8 ++++----
 1 file changed, 4 insertions(+), 4 deletions(-)

diff --git a/MuPoMo_normalization/Metainfo.txt b/MuPoMo_normalization/Metainfo.txt
index 6b7884e..5f8975c 100644
--- a/MuPoMo_normalization/Metainfo.txt
+++ b/MuPoMo_normalization/Metainfo.txt
@@ -3,12 +3,12 @@ Name of QuantLet :  MuPoMo_normalization
 Published in :      MuPoMo
 
 Description :      'Normalizes optimal shape variation parameters theta estimated from MuPoMo_optimization, and will be 
-                    called in MuPoMo_main_multipop.’
+                    called in MuPoMo_main_multipop.'
 
-Keywords :         ‘time series, demography, mortality, population, normalization’
+Keywords :         'time series, demography, mortality, population, normalization'
 
-See also :         ‘MuPoMo_data, MuPoMo_optimization, MuPoMo_referencecurve, 
-                    MuPoMo_main_twopop, MuPoMo_main_multipop, MuPoMo_bootstrap’
+See also :         'MuPoMo_data, MuPoMo_optimization, MuPoMo_referencecurve, 
+                    MuPoMo_main_twopop, MuPoMo_main_multipop, MuPoMo_bootstrap'
 
 Author :            Lei Fang
 

From 70736b4d25d3e891be4a53daa4e9a9e070c95a64 Mon Sep 17 00:00:00 2001
From: Lei Fang <LFlvb@users.noreply.github.com>
Date: Fri, 17 Jun 2016 13:48:59 +0200
Subject: [PATCH 18/63] Update Metainfo.txt

---
 MuPoMo_optimization/Metainfo.txt | 8 ++++----
 1 file changed, 4 insertions(+), 4 deletions(-)

diff --git a/MuPoMo_optimization/Metainfo.txt b/MuPoMo_optimization/Metainfo.txt
index 3586057..39d4310 100644
--- a/MuPoMo_optimization/Metainfo.txt
+++ b/MuPoMo_optimization/Metainfo.txt
@@ -3,12 +3,12 @@ Name of QuantLet :  MuPoMo_optimization
 Published in :      MuPoMo
 
 Description :      'Optimizes shape variation parameters theta based on kt and reference curve 
-                    to update new kt, and will be called in MuPoMo_main_twopop and MuPoMo_main_multipop.’
+                    to update new kt, and will be called in MuPoMo_main_twopop and MuPoMo_main_multipop.'
 
-Keywords :         ‘time series, demography, mortality, population, nonlinear, optimization, non parametric smoothing’
+Keywords :         'time series, demography, mortality, population, nonlinear, optimization, non parametric smoothing'
 
-See also :         ‘MuPoMo_data, MuPoMo_normalization, MuPoMo_referencecurve, 
-                    MuPoMo_main_twopop, MuPoMo_main_multipop, MuPoMo_bootstrap’
+See also :         'MuPoMo_data, MuPoMo_normalization, MuPoMo_referencecurve, 
+                    MuPoMo_main_twopop, MuPoMo_main_multipop, MuPoMo_bootstrap'
 
 Author :            Lei Fang, Juhyun Park
 

From f06e56efd7484dd48a3c5f95dc0d9130aad075a6 Mon Sep 17 00:00:00 2001
From: Lei Fang <LFlvb@users.noreply.github.com>
Date: Fri, 17 Jun 2016 13:49:40 +0200
Subject: [PATCH 19/63] Update Metainfo.txt

---
 MuPoMo_referencecurve/Metainfo.txt | 8 ++++----
 1 file changed, 4 insertions(+), 4 deletions(-)

diff --git a/MuPoMo_referencecurve/Metainfo.txt b/MuPoMo_referencecurve/Metainfo.txt
index 3900ea6..73c8655 100644
--- a/MuPoMo_referencecurve/Metainfo.txt
+++ b/MuPoMo_referencecurve/Metainfo.txt
@@ -3,12 +3,12 @@ Name of QuantLet :  MuPoMo_referencecurve
 Published in :      MuPoMo
 
 Description :      'Regenerates reference curve (common trend) based on normalized optimal theta parameters and smoothed original kt, 
-                    and will be called in MuPoMo_main_multipop.’
+                    and will be called in MuPoMo_main_multipop.'
 
-Keywords :         ‘time series, demography, mortality, population, normalization’
+Keywords :         'time series, demography, mortality, population, normalization'
 
-See also :         ‘MuPoMo_data, MuPoMo_optimization, MuPoMo_normalization, 
-                    MuPoMo_main_twopop, MuPoMo_main_multipop, MuPoMo_bootstrap’
+See also :         'MuPoMo_data, MuPoMo_optimization, MuPoMo_normalization, 
+                    MuPoMo_main_twopop, MuPoMo_main_multipop, MuPoMo_bootstrap'
 
 Author :            Lei Fang
 

From fc7e77b9233d688d86fcbe143ee7b34abbb9631d Mon Sep 17 00:00:00 2001
From: Lukas Borke <admin@quantnet.technology>
Date: Fri, 17 Jun 2016 16:53:44 +0200
Subject: [PATCH 20/63] auto create md

---
 MuPoMo_bootstrap/README.md | 240 +++++++++++++++++++++++++++++++++++++
 1 file changed, 240 insertions(+)
 create mode 100644 MuPoMo_bootstrap/README.md

diff --git a/MuPoMo_bootstrap/README.md b/MuPoMo_bootstrap/README.md
new file mode 100644
index 0000000..bdb9f49
--- /dev/null
+++ b/MuPoMo_bootstrap/README.md
@@ -0,0 +1,240 @@
+
+[<img src="https://github.com/QuantLet/Styleguide-and-FAQ/blob/master/pictures/banner.png" width="880" alt="Visit QuantNet">](http://quantlet.de/index.php?p=info)
+
+## [<img src="https://github.com/QuantLet/Styleguide-and-Validation-procedure/blob/master/pictures/qloqo.png" alt="Visit QuantNet">](http://quantlet.de/) **MuPoMo_bootstrap** [<img src="https://github.com/QuantLet/Styleguide-and-Validation-procedure/blob/master/pictures/QN2.png" width="60" alt="Visit QuantNet 2.0">](http://quantlet.de/d3/ia)
+
+```yaml
+
+Name of QuantLet : MuPoMo_bootstrap
+
+Published in : MuPoMo
+
+Description : 'Forecasts mortality rates based on a semi-parametric approach, and bootstraps time
+series with innovation to compute the prediction intervals. Uses random two countries to
+demonstrate.'
+
+Keywords : 'time series, demography, mortality, population, nonparametric smoothing, parametric
+modelling, Lee-Carter method, bootstrap'
+
+See also : 'MuPoMo_data, MuPoMo_optimization, MuPoMo_normalization, MuPoMo_referencecurve,
+MuPoMo_main_twopop, MuPoMo_main_multipop'
+
+Author : Lei Fang
+
+Submitted : Mon, June 13 2016 by Lei Fang
+
+Example : Prediction intervals at different levels, Histogram of theta1
+
+```
+
+![Picture1](Histogram of theta1.png)
+
+![Picture2](Prediction intervals at different levels.png)
+
+
+### R Code:
+```r
+# clear history and close windows
+rm(list=ls(all=TRUE))
+graphics.off()
+
+# please set working directory
+# setwd("C:/...")     # windows
+# setwd("/Users/...") # mac os
+# setwd("~/...")      # linux
+
+# install packages
+library(demography)
+library(rgl)
+library(sm)
+library(boot)
+library(tseries)
+
+# setting
+par(mar = c(5, 5, 2, 2), cex.axis = 1.5, cex.lab = 2)
+options(digits = 4)
+
+# load saved RData to reduce code-running time from previous procedure (MuPoMo_main_multipop.R)
+# load("~/.../MuPoMo_main_multipop.RData")
+
+# Bootstrap to resample from China's mortality time series to construct the CI for shape deviation parameters theta
+
+# Reference time series curve (unchanged). We use for comparing with resampled Japan's mortality TS
+kt.referencet = reference4
+# Original Japan's mortality TS, from which we are going to take TS bootstrap
+boot.data     = kt.Japan.female
+# Initialize theta values for optimazation
+theta         = theta4[16, ]
+
+### loss function
+loss = function(theta, t, kt, t.reference, kt.reference) {
+    ## assume theta[1]>0, theta[3]>0, if not, take absolute values
+    theta1 = abs(theta[1])
+    theta2 = theta[2]
+    theta3 = abs(theta[3])
+    
+    if (theta[1] < 0 | theta[3] < 0) 
+        warning("theta1 or theta3 <0, abs value is used")
+    # time adjustment
+    sm.t = (t.reference - theta2)/theta3  
+    ## common domain for kt and time-adjusted kt.reference
+    tmin = max(min(t), min(sm.t))
+    tmax = min(max(t), max(sm.t))
+    # index for common domain
+    i0 = which(t >= tmin & t <= tmax)
+    
+    if (length(i0) > 0) {
+        t0 = t[i0]
+        ## smooth interpolation of shifted kt.reference on common grid
+        dref = data.frame(sm.t = sm.t, kt.reference = kt.reference)
+        
+        # sm: sm.regression with optimal smoothing parameter 
+        h.optimal3 = h.select(sm.t, kt.reference) 
+        sm = sm.regression(sm.t, kt.reference, h = h.optimal3, eval.points = t0, model = 'none', poly.index = 1, display = 'none') 
+        mu = theta1 * sm$estimate
+
+        ## mean squared error at common grid points
+        mse = mean((kt[i0] - mu)^2)  # mse of kt and the modelled one
+    } else {
+        mse = 1e+09
+    }
+    return(mse)
+}
+
+# Construct the 'statistic' function which is needed and very important in 'tsboot' tsboot (tseries, statistic, R, l = NULL, sim =
+# 'model',...)
+boot.func = function(kt) {
+    t = time(kt)
+    t.reference = time(kt.reference)
+    ### parameter estimation
+    conv   = 1
+    theta0 = theta
+    while (conv != 0) {
+        # check convergence
+        out    = optim(theta0, loss, gr = NULL, t, kt, t.reference, kt.reference, control = list(maxit = 1000))  # optimization
+        conv   = out$convergence
+        theta0 = out$par
+    }
+    # add constraint on theta2
+    if (out$par[2] >= -200 & out$par[2] <= 200) 
+        temp.par = out$par else temp.par = theta
+    result = c(temp.par, out$value, out$convergence)
+}
+
+# simulate time series with innovation
+bootdata.fit = auto.arima(boot.data)
+sim = 500
+plot(boot.data, xlab = "Time", ylab = "Kt", ylim = c(-150, 70), col = "blue", lwd = 10)
+
+for (i in 1:sim) {
+    nam5  = paste("sim.ts", i, sep = ".")
+    # simulate time seriese based on bootstrap of innovation/error term in ARIMA fitting model
+    temp5 = simulate(bootdata.fit, nsim = length(boot.data), future = FALSE, bootstrap = TRUE)
+    assign(nam5, temp5)
+    # time series test on plot
+    lines(temp5, col = "grey")
+}
+
+# compute parameters theta's based on bootstrapped time series
+theta.boot = matrix(rep(c(0, 0, 0, 0, 0), sim), sim, 5, byrow = TRUE)
+
+for (i in 1:sim) {
+    theta.boot[i, ] = boot.func(eval(parse(text = paste("sim.ts", i, sep = "."))))
+}
+
+# plot test
+hist(theta.boot[, 1], xlab = "theta 1", main = "Histogram of theta 1")
+quantile(theta.boot[, 1])
+
+hist(theta.boot[, 2][which(theta.boot[, 2] >= -100 & theta.boot[, 2] <= 100)], xlab = "theta 2", 
+     main = "Histogram of theta 2", xlim = c(-5, 5), breaks = 10)
+quantile(theta.boot[, 2])
+
+hist(theta.boot[, 3][which(theta.boot[, 3] >= 0.8 & theta.boot[, 3] <= 1.2)], xlab = "theta 3", 
+     main = "Histogram of theta 3", xlim = c(0.93, 0.99), breaks = 10)
+quantile(theta.boot[, 3])
+
+# forecast with estimated parameters from bootstrap
+boot.forecast = function(theta, kt, kt.reference) {
+    t = time(kt)
+    t.reference = time(kt.reference)
+    ### check results on graph
+    theta1 = abs(theta[1])
+    theta2 = theta[2]
+    theta3 = abs(theta[3])
+    # time adjustment
+    sm.t = (t.reference - theta2)/theta3
+    ## common grid for kt and shifted kt.reference
+    tmin = max(min(t), min(sm.t))
+    tmax = min(max(t), max(sm.t))
+    i0   = which(t >= tmin & t <= tmax)
+    t0   = t[i0]
+    ## shifted curves (kt.hat)
+    dref = data.frame(sm.t = sm.t, kt.reference = kt.reference)
+    # sm: sm.regression with optimal smoothing parameter
+    h.optimal4 = h.select(sm.t, kt.reference)
+    sm = sm.regression(sm.t, kt.reference, h = h.optimal4, eval.points = sm.t, model = "none", poly.index = 1, display = "none")
+    mu = theta1 * sm$estimate
+
+    mu = ts(mu, start = sm.t[1], frequency = theta3)
+    
+    # sm: sm.regression with optimal smoothing parameter
+    h.optimal5 = h.select(sm.t, kt.reference)
+    sm0 = sm.regression(sm.t, kt.reference, h = h.optimal5, eval.points = t0, model = "none", poly.index = 1, display = "none")
+    mu0 = theta1 * sm0$estimate
+
+    mu0 = ts(mu0, start = t0[1], frequency = 1)
+    
+    return(list(mu, mu0, tmin, tmax))
+}
+
+# forecast
+plot(forecast(bootdata.fit, h = 40, level = 95), xlab = "Time", ylab = "Kt", xlim = c(1828, 2050), ylim = c(-200, 150))
+lines(kt.referencet, col = "blue", lwd = 5)
+lines(boot.data, col = "red", lwd = 5)
+
+for (i in 1:sim) {
+    temp  = boot.forecast(theta.boot[i, 1:3], boot.data, kt.reference)
+    nam12 = paste("shift.kt.boot", i, sep = ".")
+    assign(nam12, temp[[2]])
+    nam15 = paste("mu.boot", i, sep = ".")
+    assign(nam15, temp[[1]])
+    lines(temp[[2]], col = "green")  
+    lines(temp[[1]], col = "grey")  
+}
+
+# prediction interval
+for (i in 2010:2050) {
+    nam = matrix(0, 1, 500)
+    for (j in 1:sim) {
+        if (max(time(eval(parse(text = paste("mu.boot", j, sep = "."))))) >= i) 
+            nam[j] = window(eval(parse(text = paste("mu.boot", j, sep = "."))), i)[1] else nam[j] = NA
+    }
+    nam1 = paste("ts", i, sep = ".")
+    assign(nam1, nam)
+    nam2 = paste("ts", i, 5, sep = ".")
+    assign(nam2, quantile(nam, probs = seq(0, 1, 0.05), na.rm = T)[2])
+    nam3 = paste("ts", i, 95, sep = ".")
+    assign(nam3, quantile(nam, probs = seq(0, 1, 0.05), na.rm = T)[20])
+    nam4 = paste("ts", i, 20, sep = ".")
+    assign(nam4, quantile(nam, probs = seq(0, 1, 0.05), na.rm = T)[5])
+    nam5 = paste("ts", i, 80, sep = ".")
+    assign(nam5, quantile(nam, probs = seq(0, 1, 0.05), na.rm = T)[17])
+}
+
+for (j in c(5, 20, 80, 95)) {
+    ts.temp = ts(0, start = 2010, end = 2040, frequency = 1)
+    for (i in 2010:2040) {
+        ts.temp[i - 2009] = eval(parse(text = paste("ts", i, j, sep = ".")))
+    }
+    nam6 = paste("ts.forecast", j, sep = ".")
+    assign(nam6, ts.temp)
+}
+
+# plot
+plot(boot.data, lwd = 5, xlab = "Time", ylab = "Kt", xlim = c(1828, 2050), ylim = c(-200, 150))
+polygon(c(2010:2040, rev(2010:2040)), c(ts.forecast.5, rev(ts.forecast.95)), col = "yellow", border = FALSE)
+polygon(c(2010:2040, rev(2010:2040)), c(ts.forecast.20, rev(ts.forecast.80)), col = "Gray", border = FALSE)
+lines(kt.referencet, col = "blue", lwd = 5)
+lines(mu.China.4, col = 5, lty = 2, lwd = 4)
+```

From 2bdad359bd67398f2b3427193ffa0224273a3487 Mon Sep 17 00:00:00 2001
From: Lukas Borke <admin@quantnet.technology>
Date: Fri, 17 Jun 2016 16:53:45 +0200
Subject: [PATCH 21/63] auto create md

---
 MuPoMo_data/README.md | 59 +++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 59 insertions(+)
 create mode 100644 MuPoMo_data/README.md

diff --git a/MuPoMo_data/README.md b/MuPoMo_data/README.md
new file mode 100644
index 0000000..94fea62
--- /dev/null
+++ b/MuPoMo_data/README.md
@@ -0,0 +1,59 @@
+
+[<img src="https://github.com/QuantLet/Styleguide-and-FAQ/blob/master/pictures/banner.png" width="880" alt="Visit QuantNet">](http://quantlet.de/index.php?p=info)
+
+## [<img src="https://github.com/QuantLet/Styleguide-and-Validation-procedure/blob/master/pictures/qloqo.png" alt="Visit QuantNet">](http://quantlet.de/) **MuPoMo_data** [<img src="https://github.com/QuantLet/Styleguide-and-Validation-procedure/blob/master/pictures/QN2.png" width="60" alt="Visit QuantNet 2.0">](http://quantlet.de/d3/ia)
+
+```yaml
+
+Name of QuantLet : MuPoMo_data
+
+Published in : MuPoMo
+
+Description : 'Reads data from Human Mortality Database and calculate kt, and will be called in
+MuPoMo_main_twopop and MuPoMo_main_multipop.'
+
+Keywords : 'time series, demography, mortality, Lee-Carter method, population, Human Mortality
+Database'
+
+See also : 'MuPoMo_optimization, MuPoMo_normalization, MuPoMo_referencecurve, MuPoMo_main_twopop,
+MuPoMo_main_multipop, MuPoMo_bootstrap'
+
+Author : Lei Fang
+
+Submitted : Mon, June 13 2016 by Lei Fang
+
+```
+
+
+### R Code:
+```r
+# read multi-pop female mortality rates from Human Mortality Database
+shortnames.all = c("AUS", "AUT", "BLR", "BGR", "CAN", "CHL", "CZE", "DNK", "EST", "FIN", "FRATNP", "DEUTNP", "HUN", "ISL", "IRL", 
+    "ISR", "ITA", "JPN", "LVA", "LTU", "LUX", "NLD", "NZL_NP", "NOR", "POL", "PRT", "RUS", "SVK", "SVN", "ESP", "CHE", "TWN", "GBR_NP", 
+    "USA", "SWE")
+names.all = c("Australia", "Austria", "Belarus", "Bulgaria", "Canada", "Chile", "CzechRepublic", "Denmark", "Estonia", "Finland", 
+    "France", "Germany", "Hungary", "Iceland", "Ireland", "Israel", "Italy", "Japan", "Latvia", "Lithuania", "Luxembourg", "Netherlands", 
+    "NewZealand", "Norway", "Poland", "Portugal", "Russia", "Slovakia", "Slovenia", "Spain", "Switzerland", "Taiwan", "UnitedKingdom", 
+    "USA", "Sweden")
+
+loop.all = length(names.all)
+for (i in 1:loop.all) {
+    nam1 = paste(names.all[i])
+    # read data from Human Mortality Database (HMD: http://www.mortality.org/)
+    # you need register on HMD to access a free account accound and set up your password
+    assign(nam1, hmd.mx(shortnames.all[i], "account", "password", names.all[i]))
+    temp1 = hmd.mx(shortnames.all[i], "account", "password", names.all[i])
+    nam2  = paste(names.all[i], "lca.female", sep = ".")
+    # Lee-Carter method
+    assign(nam2, lca(temp1, series = "female", adjust = "dt", interpolate = TRUE))
+    temp2 = lca(temp1, series = "female", adjust = "dt", interpolate = TRUE)
+    nam3  = paste("ax", names.all[i], "female", sep = ".")  # ax
+    assign(nam3, temp2$ax)
+    nam4  = paste("bx", names.all[i], "female", sep = ".")  # bx
+    assign(nam4, temp2$bx)
+    nam5  = paste("kt", names.all[i], "female", sep = ".")  # kt
+    assign(nam5, temp2$kt)
+}
+
+
+```

From 7f61746bfffcbe6fe54fcf620d5b4536b8cebf6c Mon Sep 17 00:00:00 2001
From: Lukas Borke <admin@quantnet.technology>
Date: Fri, 17 Jun 2016 16:53:45 +0200
Subject: [PATCH 22/63] auto create md

---
 MuPoMo_main_multipop/README.md | 192 +++++++++++++++++++++++++++++++++
 1 file changed, 192 insertions(+)
 create mode 100644 MuPoMo_main_multipop/README.md

diff --git a/MuPoMo_main_multipop/README.md b/MuPoMo_main_multipop/README.md
new file mode 100644
index 0000000..baccb3e
--- /dev/null
+++ b/MuPoMo_main_multipop/README.md
@@ -0,0 +1,192 @@
+
+[<img src="https://github.com/QuantLet/Styleguide-and-FAQ/blob/master/pictures/banner.png" width="880" alt="Visit QuantNet">](http://quantlet.de/index.php?p=info)
+
+## [<img src="https://github.com/QuantLet/Styleguide-and-Validation-procedure/blob/master/pictures/qloqo.png" alt="Visit QuantNet">](http://quantlet.de/) **MuPoMo_main_multipop** [<img src="https://github.com/QuantLet/Styleguide-and-Validation-procedure/blob/master/pictures/QN2.png" width="60" alt="Visit QuantNet 2.0">](http://quantlet.de/d3/ia)
+
+```yaml
+
+Name of QuantLet : MuPoMo_main_multipop
+
+Published in : MuPoMo
+
+Description : 'Estimates and forecasts mortality rates based on a semi-parametric approach, which
+applies parametric modelling for multiple nonparametric smoothed curves with the shape-related
+nonlinear variation.'
+
+Keywords : 'time series, demography, mortality, population, nonparametric smoothing, parametric
+modelling, Lee-Carter method'
+
+See also : 'MuPoMo_data, MuPoMo_optimization, MuPoMo_normalization, MuPoMo_referencecurve,
+MuPoMo_main_twopop, MuPoMo_bootstrap'
+
+Author : Lei Fang
+
+Submitted : Mon, June 13 2016 by Lei Fang
+
+Example : Multi-Population model with German data, Multi-Population model with Japanese data
+
+```
+
+![Picture1](Multi-Population model with German data.png)
+
+![Picture2](Multi-Population model with Japanese data.png)
+
+
+### R Code:
+```r
+# clear history and close windows
+rm(list=ls(all=TRUE))
+graphics.off()
+
+# please set working directory
+# setwd("C:/...")     # windows
+# setwd("/Users/...") # mac os
+# setwd("~/...")      # linux
+
+# install packages
+library(demography)
+library(rgl)
+library(sm)
+
+# set plot
+par(mar = c(5, 5, 2, 2), cex.axis = 1.5, cex.lab = 2)
+
+# recall self-defined functions
+source('MuPoMo_data.R')
+source("MuPoMo_optimization.R")
+source("MuPoMo_normalization.R")
+source("MuPoMo_referencecurve.R")
+
+# set bandwidth
+bw.default = 2.5
+
+## descriptive plot plot kt of 35 countries
+plot(kt.Sweden.female, type = "l", ylim = c(-250, 150), xlab = "Time", ylab = "kt", main = "Original Kt (35 countries)")
+for (i in 1:(loop.all - 1)) {
+    lines(eval(parse(text  = paste("kt.", names.all[i], ".female", sep = ""))), col = i)
+}
+
+##### common trend
+#### initial setting nonparametric smoothing 35 countries
+for (i in 1:loop.all) {
+    kt = eval(parse(text = paste("kt.", names.all[i], ".female", sep = "")))
+    t  = eval(parse(text = paste(names.all[i])))$year
+    d  = data.frame(kt, t)
+    # sm: sm.regression with optimal smoothing parameter
+    h.optimal1 = h.select(t, kt)
+    sm         = sm.regression(t, kt, h = h.optimal1, eval.points = t, model = "none", poly.index = 1, display = "none")
+    nam6       = paste("sm.kt", names.all[i], "female", sep = ".")
+    temp6      = ts(sm$estimate, start = t[1], frequency = 1)
+    assign(nam6, temp6)
+}
+
+## plot smoothed kt of 35 countries
+plot(sm.kt.Sweden.female, type = "l", ylim = c(-250, 150), xlab = "Time", ylab = "kt", main = "Smoothed Kt (35 countries)")
+for (i in 1:(loop.all - 1)) {
+    lines(eval(parse(text = paste("sm.kt.", names.all[i], ".female", sep = ""))), col = i)
+}
+
+#### intial values of thetas 
+### remove Russia, Lithuavia, Latvia, Estonia and Belarus 
+### set up the initial reference curve based on 31 countries
+names.31 = c("Australia", "Austria", "Bulgaria", "Canada", "Chile", "CzechRepublic", "Denmark", "Finland", "France", "Germany", "Hungary", 
+    "Iceland", "Ireland", "Israel", "Italy", "Japan", "Luxembourg", "Netherlands", "NewZealand", "Norway", "Poland", "Portugal", "Slovakia", 
+    "Slovenia", "Spain", "Switzerland", "Taiwan", "UnitedKingdom", "USA", "Sweden")
+loop.31  = length(names.31)
+merge1   = sm.kt.Australia.female
+for (i in 1:(loop.31 - 1)) {
+    nam7  = paste("merge", i + 1, sep = "")
+    temp3 = merge.zoo(eval(parse(text = paste("merge", i, sep = ""))), eval(parse(text = paste("sm.kt.", names.31[i + 1], ".female", 
+        sep = ""))))
+    assign(nam7, temp3)
+}
+reference0.temp = rowMeans(merge31, na.rm = TRUE)
+reference0      = ts(reference0.temp, start = Sweden$year[1], frequency = 1)
+
+## plot the reference curve among all 31 smoothed curves
+plot(sm.kt.Sweden.female, type = "l", ylim = c(-250, 150), xlab = "Time", ylab = "kt", main = "Reference Curve vs. Smoothed Kt (31 countries)")
+for (i in 1:loop.31) {
+    lines(eval(parse(text = paste("sm.kt.", names.31[i], ".female", sep = ""))), col = i)
+}
+lines(reference0, lwd = 4, col = "red")
+
+##### begin loop
+theta0    = matrix(rep(c(1, 0, 1), loop.31), loop.31, 3, byrow = TRUE)
+iteration = 5
+for (j in 1:iteration) {
+    ### find the optimal initial theta based on the reference curve
+    theta        = eval(parse(text = paste("theta", j - 1, sep = "")))
+    kt.reference = eval(parse(text = paste("reference", j - 1, sep = "")))
+    results      = matrix(NA, loop.31, 5)  # c(theta1,theta2,theta3, loss, convergence)
+    for (i in 1:loop.31) {
+        kt           = eval(parse(text = paste("sm.kt.", names.31[i], ".female", sep = "")))
+        tt           = time(kt)
+        ltt          = length(tt)
+        temp4        = optimization(theta[i, ], kt, kt.reference)
+        results[i, ] = temp4[[1]]
+        nam12        = paste("shift.kt", names.31[i], j, sep = ".")
+        assign(nam12, temp4[[3]])
+        nam15        = paste("mu", names.31[i], j, sep = ".")
+        assign(nam15, temp4[[2]])
+        pdf(paste("plot_", j, "_", i, ".pdf", sep = ""))
+        par(mar = c(5, 5, 2, 2))
+        plot(eval(parse(text = paste("kt.", names.31[i], ".female", sep = ""))), ylim = c(-250, 150), xlim = c(1750, 2020), type = "p", 
+            xlab = "Time", ylab = "kt", main = paste(names.31[i], tt[1], "--", tt[ltt], ":step", j))
+        lines(kt, col = 2)  # sm.kt
+        lines(kt.reference, col = 4, lwd = 2)  # reference
+        lines(temp4[[2]], col = 5, lty = 5)  # new kt
+        lines(temp4[[3]], col = 5, lwd = 2)  # new kt
+        abline(v = temp4[[4]], col = "gray", lty = 5)
+        abline(v = temp4[[5]], col = "gray", lty = 5)
+        # legend('topright', legend=c('kt', 'sm.kt', 'k0', 'kt.hat'), col=c(1,2,4,5), lty=1)
+        dev.off()
+    }
+    nam16 = paste("results", j, sep = "")
+    assign(nam16, results)
+    nam18 = paste("theta", j, sep = "")
+    assign(nam18, results[, 1:3])
+    
+    ## plot shifted kt of 31 countries and the reference curve of previous step
+    plot(kt.reference, type = "l", ylim = c(-250, 150), xlab = "Time", ylab = "kt", lwd = 4, col = "red", main = paste("Reference Curve vs. Shifted Kt (31 countries): step", 
+        j - 1))
+    for (i in 1:loop.31) {
+        lines(eval(parse(text = paste("shift.kt", names.31[i], j, sep = "."))), col = i)
+    }
+    
+    # construct optimal.theta.matrix and normalize optimal theta
+    optimal.theta.matrix          = results[, 1:3]
+    standard.optimal.theta.matrix = normalization(optimal.theta.matrix)
+    
+    # construct new reference curve
+    for (i in 1:loop.31) {
+        nam13 = paste("shift.kt", names.31[i], "standard", sep = ".")
+        assign(nam13, referencecurve(standard.optimal.theta.matrix[i, 2], standard.optimal.theta.matrix[i, 3], eval(parse(text = paste("sm.kt.", 
+            names.31[i], ".female", sep = ""))), eval(parse(text = paste("shift.kt", names.31[i], j, sep = ".")))))
+    }
+    merge1.1  = shift.kt.Australia.standard
+    for (i in 1:(loop.31 - 1)) {
+        nam7  = paste("merge1", i + 1, sep = ".")
+        temp3 = merge.zoo(eval(parse(text = paste("merge1", i, sep = "."))), eval(parse(text = paste("shift.kt", names.31[i + 1], 
+            "standard", sep = "."))))
+        assign(nam7, temp3)
+    }
+    reference.temp           = rowMeans(merge1.31, na.rm = TRUE)
+    reference.temp.nonsmooth = ts(reference.temp, start = min(index(merge1.31)), frequency = 1)
+    t.temp                   = time(reference.temp.nonsmooth)
+    
+    ## smooth the updated reference curve
+    # sm: sm.regression
+    temp17 = sm.regression(t.temp, reference.temp.nonsmooth, eval.points = t.temp, model = "none", poly.index = 1, display = "none")
+    nam17  = paste("reference", j, sep = "")
+    assign(nam17, ts(temp17$estimate, start = t.temp[1], frequency = 1))
+    
+    ## plot the updated reference curve among all 31 shifted curves
+    plot(eval(parse(text = paste("reference", j, sep = ""))), lwd = 4, col = "red", type = "l", ylim = c(-250, 150), xlab = "Time", 
+        ylab = "kt", main = paste("Updated Reference Curve vs. Shifted Kt (31 countries): step", j))
+    for (i in 1:loop.31) {
+        lines(eval(parse(text = paste("shift.kt", names.31[i], j, sep = "."))), col = i)
+        lines(eval(parse(text = paste("sm.kt.", names.31[i], ".female", sep = ""))), col = "grey")
+    }
+    lines(eval(parse(text = paste("reference", j - 1, sep = ""))), col = "blue", lwd = 3, lty = 5)
+}
+```

From eb3936bdc22848b6542209e27d480d4de9cedabf Mon Sep 17 00:00:00 2001
From: Lukas Borke <admin@quantnet.technology>
Date: Fri, 17 Jun 2016 16:53:46 +0200
Subject: [PATCH 23/63] auto create md

---
 MuPoMo_main_twopop/README.md | 195 +++++++++++++++++++++++++++++++++++
 1 file changed, 195 insertions(+)
 create mode 100644 MuPoMo_main_twopop/README.md

diff --git a/MuPoMo_main_twopop/README.md b/MuPoMo_main_twopop/README.md
new file mode 100644
index 0000000..74e74bb
--- /dev/null
+++ b/MuPoMo_main_twopop/README.md
@@ -0,0 +1,195 @@
+
+[<img src="https://github.com/QuantLet/Styleguide-and-FAQ/blob/master/pictures/banner.png" width="880" alt="Visit QuantNet">](http://quantlet.de/index.php?p=info)
+
+## [<img src="https://github.com/QuantLet/Styleguide-and-Validation-procedure/blob/master/pictures/qloqo.png" alt="Visit QuantNet">](http://quantlet.de/) **MuPoMo_main_twopop** [<img src="https://github.com/QuantLet/Styleguide-and-Validation-procedure/blob/master/pictures/QN2.png" width="60" alt="Visit QuantNet 2.0">](http://quantlet.de/d3/ia)
+
+```yaml
+
+Name of QuantLet : MuPoMo_main_twopop
+
+Published in : MuPoMo
+
+Description : 'Estimates and forecasts mortality rates based on a semi-parametric approach, which
+applies parametric modelling for multiple nonparametric curves with the shape-related nonlinear
+variation. Uses random two countries to demonstrate two-country case.'
+
+Keywords : 'time series, demography, mortality, population, nonparametric smoothing, parametric
+modelling, Lee-Carter method, contour'
+
+See also : 'MuPoMo_data, MuPoMo_optimization, MuPoMo_normalization, MuPoMo_referencecurve,
+MuPoMo_main_multipop, MuPoMo_bootstrap'
+
+Author : Lei Fang
+
+Submitted : Mon, June 13 2016 by Lei Fang
+
+Example : 'Time shift at different levels, Loss function of theta2, Loss surface 3D, Contour plot
+of theta2 and theta4, Model fit and forecast'
+
+```
+
+![Picture1](Contour plot of theta2 and theta4.png)
+
+![Picture2](Loss function of theta2.png)
+
+![Picture3](Loss surface 3D.png)
+
+![Picture4](Model fit and forecast.png)
+
+![Picture5](Time shift at different levels.png)
+
+
+### R Code:
+```r
+# clear history and close windows
+rm(list=ls(all=TRUE))
+graphics.off()
+
+# please set working directory
+# setwd("C:/...")     # windows
+# setwd("/Users/...") # mac os
+# setwd("~/...")      # linux
+
+# install packages
+library(demography)
+library(rgl)
+library(sm)
+
+# set plot
+par(mar = c(5, 5, 2, 2), cex.axis = 1.5, cex.lab = 2)
+
+# recall self-defined functions
+# read data and compute kt based on Lee-Carter Model via source('data.R')
+source('MuPoMo_data.R')
+source("MuPoMo_optimization.R")
+
+# choose two countries' kt for this analysis
+kt1 = kt.China.female
+kt2 = kt.Japan.female
+
+# set bandwidth for smoothing curves
+bw.default     = 2.5
+
+# plot kt
+plot(kt2, type = "l", col = "blue", lwd = 4, xlab = "Time", ylab = "Kt")
+lines(kt1, col = "red", lwd = 4)
+
+# shift movement of the two smoothed countries
+t1         = 1994:2010 # differ based on the chosen country
+d1         = data.frame(time(kt1), kt1)
+h.optimal1 = h.select(time(kt1), kt1)
+sm1        = sm.regression(time(kt1), kt1, h = h.optimal1, eval.points = time(kt1), model = "none", poly.index = 1, display = "none")
+sm.kt1     = sm1$estimate  # smoothed kt1
+
+t2         = 1947:2012 # differ based on the chosen country
+d2         = data.frame(time(kt2), kt2)
+h.optimal2 = h.select(time(kt2), kt2)
+sm2        = sm.regression(time(kt2), kt2, h = h.optimal2, eval.points = time(kt2), model = "none", poly.index = 1, display = "none")
+sm.kt2     = sm2$estimate  # smoothed kt2
+
+plot(t2, sm.kt2, type = "l", col = "blue", lwd = 4, xlab = "Time", ylab = "Kt")
+lines(kt2, col = "red", lwd = 4)
+lines(t1, sm.kt1, lwd = 4)
+lines(kt1, col = "darkgreen", lwd = 4)
+lines(t2 + 20, sm.kt2, lwd = 4, lty = 2) # differ based on the chosen country
+lines(t2 + 25, sm.kt2, lwd = 4, lty = 3)
+lines(t2 + 30, sm.kt2, lwd = 4, lty = 4)
+
+# time delay
+plot(t2, sm.kt2, type = "l", col = "blue", lwd = 4, xlab = "Time", ylab = "Kt")
+lines(t1, sm.kt1, lwd = 4)
+lines(t2 + 23, sm.kt2, lwd = 4, lty = 4, col = "blue") # differ based on the chosen country
+
+# vertical shift
+plot(t2, sm.kt2, type = "l", col = "blue", lwd = 4, xlab = "Time", ylab = "Kt")
+lines(t1, sm.kt1, lwd = 4)
+lines(t2, sm.kt2 + 85, lwd = 4, lty = 4, col = "blue") # differ based on the chosen country
+
+# optimization
+theta.2pop  = c(1, -23, 1) # differ based on the chosen country
+result.2pop = optimization(theta.2pop, kt1, kt2)
+
+# plot optimized movement
+plot(t2, sm.kt2, type = "l", col = 4, lwd = 4, xlab = "Time", ylab = "Kt")
+lines(kt2, type = "p", lwd = 3)
+lines(t1, sm.kt1, lwd = 4, col = 2)
+lines(kt1, type = "p", lwd = 3)
+lines(result.2pop[[2]], col = 5, lty = 5)  #
+lines(result.2pop[[3]], col = 5, lwd = 3)  #
+abline(v = result.2pop[[4]], col = "gray", lty = 5)
+abline(v = result.2pop[[5]], col = "gray", lty = 5)
+
+# plot loss function
+loss = function(theta1, theta2, theta3, theta4, t, kt, t.reference, kt.reference) {
+    sm.t = (t.reference - theta2)/theta3  # time adjustment
+    ## common domain for kt and time-adjusted kt.reference
+    tmin = max(min(t), min(sm.t))
+    tmax = min(max(t), max(sm.t))
+    i0 = which(t >= tmin & t <= tmax)  # index for common domain
+    if (length(i0) > 0) {
+        t0 = t[i0]
+        ## smooth interpolation of shifted kt.reference on common grid
+        dref = data.frame(sm.t = sm.t, kt.reference = kt.reference)
+        # sm: sm.regression with optimal smoothing parameter
+        h.optimal3 = h.select(sm.t, kt.reference)
+        sm = sm.regression(sm.t, kt.reference, h = h.optimal3, eval.points = t0, model = "none", poly.index = 1, display = "none")
+        mu = theta1 * sm$estimate + theta4
+        ## mean squared error at common grid points
+        mse = mean((kt[i0] - mu)^2)  # mse of kt and the modelled one
+    } else {
+        mse = 1e+09
+    }
+    return(mse)
+}
+
+# plot loss function of theta2 and theta4
+vtheta2 = seq(-30, 10, len = 100) # differ based on the chosen country
+vtheta4 = seq(0, 100, len = 100) # differ based on the chosen country
+npar    = length(vtheta2)
+res     = matrix(rep(0, 10000), 100, 100)
+for (i in 1:npar) {
+    for (l in 1:npar) {
+        res[i, l] = loss(1, vtheta2[i], 1, vtheta4[l], t1, kt1, t2, kt2)
+    }
+    res[i, l] = loss(1, vtheta2[i], 1, vtheta4[l], t1, kt1, t2, kt2)
+}
+
+persp3d(vtheta2, vtheta4, res, col = "blue", xlab = "theta2", ylab = "theta4", zlab = "Loss")
+
+resnew = res * (res < 5000)
+persp3d(vtheta2, vtheta4, resnew, col = "blue", xlab = "theta2", ylab = "theta4", zlab = "Loss")
+
+# contour plot
+contour(vtheta2, vtheta4, resnew, col = rainbow(20), nlevels = 20, lwd = 1, xlim = c(-23, 0), ylim = c(0, 80))
+contour(vtheta2, vtheta4, res, col = rainbow(20), nlevels = 70, lwd = 1, xlim = c(-23, 0), ylim = c(0, 80), zlim = c(0, 100))
+contour(vtheta2, vtheta4, res, col = rainbow(20), nlevels = 70, lwd = 1, xlim = c(-10, -2), ylim = c(40, 80), zlim = c(0, 100))
+
+# plot loss function of theta2
+vtheta22 = seq(-50, 0, len = 100) # differ based on the chosen country
+npar2    = length(vtheta22)
+res2     = rep(0, 100)
+for (i in 1:npar2) {
+    res2[i] = loss(1, vtheta22[i], 1, 0, t1, kt1, t2, kt2)
+}
+plot(vtheta22, res2, col = "blue", xlab = "theta2", ylab = "Loss", type = "l", lwd = 4)
+
+# plot loss function of theta4
+vtheta42 = seq(40, 140, len = 100) # differ based on the chosen country
+npar3    = length(vtheta42)
+res3     = rep(0, 100)
+for (i in 1:npar3) {
+    res3[i] = loss(1, 0, 1, vtheta42[i], t1, kt1, t2, kt2)
+}
+plot(vtheta42, res3, col = "blue", xlab = "theta4", ylab = "Loss", type = "l", lwd = 4)
+
+# forecast
+plot(t2, sm.kt2, type = "l", col = 4, lwd = 4, xlab = "Time", ylab = "Kt", xlim = c(1947, 2035))
+lines(kt2, type = "p", lwd = 3)
+lines(t1, sm.kt1, lwd = 4, col = 2)
+lines(kt1, type = "p", lwd = 3)
+lines(result.2pop[[2]], col = 4, lty = 5, lwd = 3)  #
+lines(result.2pop[[3]], col = "purple", lwd = 3)  #
+abline(v = result.2pop[[4]], col = "gray", lty = 5)
+abline(v = result.2pop[[5]], col = "gray", lty = 5)
+
+```

From 2531f57f400e410e3ee93bfccf609bfbd087b276 Mon Sep 17 00:00:00 2001
From: Lukas Borke <admin@quantnet.technology>
Date: Fri, 17 Jun 2016 16:53:47 +0200
Subject: [PATCH 24/63] auto create md

---
 MuPoMo_normalization/README.md | 50 ++++++++++++++++++++++++++++++++++
 1 file changed, 50 insertions(+)
 create mode 100644 MuPoMo_normalization/README.md

diff --git a/MuPoMo_normalization/README.md b/MuPoMo_normalization/README.md
new file mode 100644
index 0000000..0751111
--- /dev/null
+++ b/MuPoMo_normalization/README.md
@@ -0,0 +1,50 @@
+
+[<img src="https://github.com/QuantLet/Styleguide-and-FAQ/blob/master/pictures/banner.png" width="880" alt="Visit QuantNet">](http://quantlet.de/index.php?p=info)
+
+## [<img src="https://github.com/QuantLet/Styleguide-and-Validation-procedure/blob/master/pictures/qloqo.png" alt="Visit QuantNet">](http://quantlet.de/) **MuPoMo_normalization** [<img src="https://github.com/QuantLet/Styleguide-and-Validation-procedure/blob/master/pictures/QN2.png" width="60" alt="Visit QuantNet 2.0">](http://quantlet.de/d3/ia)
+
+```yaml
+
+Name of QuantLet : MuPoMo_normalization
+
+Published in : MuPoMo
+
+Description : 'Normalizes optimal shape variation parameters theta estimated from
+MuPoMo_optimization, and will be called in MuPoMo_main_multipop.'
+
+Keywords : time series, demography, mortality, population, normalization
+
+See also : 'MuPoMo_data, MuPoMo_optimization, MuPoMo_referencecurve, MuPoMo_main_twopop,
+MuPoMo_main_multipop, MuPoMo_bootstrap'
+
+Author : Lei Fang
+
+Submitted : Mon, June 13 2016 by Lei Fang
+
+```
+
+
+### R Code:
+```r
+normalization  = function(theta) {
+    theta.temp = colSums(theta)
+    for (i in 1:loop.31) {
+        nam10  = paste("normal.theta", names.31[i], 1, sep = ".")
+        assign(nam10, loop.31 * theta[i, 1]/theta.temp[1])
+        nam11  = paste("normal.theta", names.31[i], 3, sep = ".")
+        assign(nam11, loop.31 * theta[i, 3]/theta.temp[3])
+        nam12  = paste("normal.theta", names.31[i], 2, sep = ".")
+        assign(nam12, theta[i, 2] - theta.temp[2]/loop.31)
+        nam14  = paste("normal.theta", names.31[i], sep = ".")
+        assign(nam14, c(eval(parse(text = paste("normal.theta", names.31[i], 1, sep = "."))), eval(parse(text = paste("normal.theta", 
+            names.31[i], 2, sep = "."))), eval(parse(text = paste("normal.theta", names.31[i], 3, sep = ".")))))
+    }
+    ll = list()
+    for (i in 1:loop.31) {
+        ll[[i]]  = c(eval(parse(text = paste("normal.theta", names.31[i], sep = "."))))
+    }
+    normal.theta = do.call(rbind, ll)
+    return(normal.theta)
+}
+
+```

From 568722565c2e2e74065ed93ca50934bb341c2c31 Mon Sep 17 00:00:00 2001
From: Lukas Borke <admin@quantnet.technology>
Date: Fri, 17 Jun 2016 16:53:47 +0200
Subject: [PATCH 25/63] auto create md

---
 MuPoMo_optimization/README.md | 108 ++++++++++++++++++++++++++++++++++
 1 file changed, 108 insertions(+)
 create mode 100644 MuPoMo_optimization/README.md

diff --git a/MuPoMo_optimization/README.md b/MuPoMo_optimization/README.md
new file mode 100644
index 0000000..77ce1b8
--- /dev/null
+++ b/MuPoMo_optimization/README.md
@@ -0,0 +1,108 @@
+
+[<img src="https://github.com/QuantLet/Styleguide-and-FAQ/blob/master/pictures/banner.png" width="880" alt="Visit QuantNet">](http://quantlet.de/index.php?p=info)
+
+## [<img src="https://github.com/QuantLet/Styleguide-and-Validation-procedure/blob/master/pictures/qloqo.png" alt="Visit QuantNet">](http://quantlet.de/) **MuPoMo_optimization** [<img src="https://github.com/QuantLet/Styleguide-and-Validation-procedure/blob/master/pictures/QN2.png" width="60" alt="Visit QuantNet 2.0">](http://quantlet.de/d3/ia)
+
+```yaml
+
+Name of QuantLet : MuPoMo_optimization
+
+Published in : MuPoMo
+
+Description : 'Optimizes shape variation parameters theta based on kt and reference curve to update
+new kt, and will be called in MuPoMo_main_twopop and MuPoMo_main_multipop.'
+
+Keywords : 'time series, demography, mortality, population, nonlinear, optimization, non parametric
+smoothing'
+
+See also : 'MuPoMo_data, MuPoMo_normalization, MuPoMo_referencecurve, MuPoMo_main_twopop,
+MuPoMo_main_multipop, MuPoMo_bootstrap'
+
+Author : Lei Fang, Juhyun Park
+
+Submitted : Mon, June 13 2016 by Lei Fang
+
+```
+
+
+### R Code:
+```r
+optimization = function(theta, kt, kt.reference) {
+           t = time(kt)
+ t.reference = time(kt.reference)
+    
+    ### loss function
+    loss = function(theta, t, kt, t.reference, kt.reference) {
+        ## assume theta[1]>0, theta[3]>0, if not, take absolute values
+        theta1 = abs(theta[1])
+        theta2 = theta[2]
+        theta3 = abs(theta[3])
+        
+        if (theta[1] < 0 | theta[3] < 0) 
+            warning("theta1 or theta3 <0, abs value is used")
+        sm.t = (t.reference - theta2)/theta3  # time adjustment
+        ## common domain for kt and time-adjusted kt.reference
+        tmin = max(min(t), min(sm.t))
+        tmax = min(max(t), max(sm.t))
+        i0   = which(t >= tmin & t <= tmax)  # index for common domain
+        if (length(i0) > 0) {
+            t0 = t[i0]
+            ## smooth interpolation of shifted kt.reference on common grid
+            dref = data.frame(sm.t = sm.t, kt.reference = kt.reference)
+            # sm: sm.regression with optimal smoothing parameter
+            h.optimal3 = h.select(sm.t, kt.reference)
+            sm = sm.regression(sm.t, kt.reference, h = h.optimal3, eval.points = t0, model = "none", poly.index = 1, display = "none")
+            mu = theta1 * sm$estimate
+            ## mean squared error at common grid points
+            mse = mean((kt[i0] - mu)^2)  # mse of kt and the modelled one
+        } else {
+            mse = 1e+09
+        }
+        return(mse)
+    }
+    
+    ### parameter estimation with nonlinear optimization
+    conv   = 1
+    theta0 = theta
+    while (conv != 0) {
+        # check convergence
+        out    = optim(theta0, loss, gr = NULL, t, kt, t.reference, kt.reference, control = list(maxit = 1000))  # optimization
+        conv   = out$convergence
+        theta0 = out$par
+    }
+    ### constraint on theta2 (time shift parameter)
+    if (out$par[2] >= -200 & out$par[2] <= 200) 
+        temp.par = out$par else temp.par = theta
+    result = c(temp.par, out$value, out$convergence)
+    
+    ### check results on graph
+    theta  = result[1:3]
+    theta1 = abs(theta[1])
+    theta2 = theta[2]
+    theta3 = abs(theta[3])
+    
+    sm.t   = (t.reference - theta2)/theta3  # time adjustment
+    ## common grid for kt and shifted kt.reference
+    tmin   = max(min(t), min(sm.t))
+    tmax   = min(max(t), max(sm.t))
+    i0     = which(t >= tmin & t <= tmax)
+    t0     = t[i0]
+    ## shifted curves (kt.hat)
+    dref   = data.frame(sm.t = sm.t, kt.reference = kt.reference)
+    
+    # sm: sm.regression with optimal smoothing parameter
+    h.optimal4 = h.select(sm.t, kt.reference)
+    sm         = sm.regression(sm.t, kt.reference, h = h.optimal4, eval.points = sm.t, model = "none", poly.index = 1, display = "none")
+    mu         = theta1 * sm$estimate
+    mu         = ts(mu, start = sm.t[1], frequency = theta3)
+    
+    # sm: sm.regression with optimal smoothing parameter
+    h.optimal5 = h.select(sm.t, kt.reference)
+    sm0        = sm.regression(sm.t, kt.reference, h = h.optimal5, eval.points = t0, model = "none", poly.index = 1, display = "none")
+    mu0        = theta1 * sm0$estimate
+    mu0        = ts(mu0, start = t0[1], frequency = 1)
+    
+    return(list(result, mu, mu0, tmin, tmax))
+}
+
+```

From b91897c474d782b83aed261afd15a1bd2ebd3271 Mon Sep 17 00:00:00 2001
From: Lukas Borke <admin@quantnet.technology>
Date: Fri, 17 Jun 2016 16:53:48 +0200
Subject: [PATCH 26/63] auto create md

---
 MuPoMo_referencecurve/README.md | 51 +++++++++++++++++++++++++++++++++
 1 file changed, 51 insertions(+)
 create mode 100644 MuPoMo_referencecurve/README.md

diff --git a/MuPoMo_referencecurve/README.md b/MuPoMo_referencecurve/README.md
new file mode 100644
index 0000000..f967c98
--- /dev/null
+++ b/MuPoMo_referencecurve/README.md
@@ -0,0 +1,51 @@
+
+[<img src="https://github.com/QuantLet/Styleguide-and-FAQ/blob/master/pictures/banner.png" width="880" alt="Visit QuantNet">](http://quantlet.de/index.php?p=info)
+
+## [<img src="https://github.com/QuantLet/Styleguide-and-Validation-procedure/blob/master/pictures/qloqo.png" alt="Visit QuantNet">](http://quantlet.de/) **MuPoMo_referencecurve** [<img src="https://github.com/QuantLet/Styleguide-and-Validation-procedure/blob/master/pictures/QN2.png" width="60" alt="Visit QuantNet 2.0">](http://quantlet.de/d3/ia)
+
+```yaml
+
+Name of QuantLet : MuPoMo_referencecurve
+
+Published in : MuPoMo
+
+Description : 'Regenerates reference curve (common trend) based on normalized optimal theta
+parameters and smoothed original kt, and will be called in MuPoMo_main_multipop.'
+
+Keywords : time series, demography, mortality, population, normalization
+
+See also : 'MuPoMo_data, MuPoMo_optimization, MuPoMo_normalization, MuPoMo_main_twopop,
+MuPoMo_main_multipop, MuPoMo_bootstrap'
+
+Author : Lei Fang
+
+Submitted : Mon, June 13 2016 by Lei Fang
+
+```
+
+
+### R Code:
+```r
+referencecurve  = function(theta2, theta3, kt, kt.null) {
+    t           = time(kt)
+    sm.t        = theta3 * t + theta2  # time adjustment
+    t.reference = Sweden$year
+    ## common grid for kt and shifted kt.reference
+    tmin = max(min(t.reference), min(sm.t))
+    tmax = min(max(t.reference), max(sm.t))
+    i0   = which(t.reference >= tmin & t.reference <= tmax)
+    if (length(i0) > 0) {
+        t0  = t.reference[i0]
+        d   = data.frame(kt, sm.t)
+        # sm: sm.regression with optimal smoothing parameter
+        h.optimal6 = h.select(sm.t, kt)
+        sm  = sm.regression(sm.t, kt, h = h.optimal6, eval.points = t0, model = "none", poly.index = 1, display = "none")
+        mu1 = sm$estimate
+        mu  = ts(mu1, start = t0[1], frequency = 1)
+    } else {
+        mu  = kt.null
+    }
+    return(mu)
+}
+
+```

From 1c970188206517aea32eb6b791a0580845c6a872 Mon Sep 17 00:00:00 2001
From: Lukas Borke <admin@quantnet.technology>
Date: Thu, 8 Dec 2016 19:46:03 +0100
Subject: [PATCH 27/63] add yamldebugger results via Yamldebugger package +
 git2r

---
 yamldebugger_results.md | 9 +++++++++
 1 file changed, 9 insertions(+)
 create mode 100644 yamldebugger_results.md

diff --git a/yamldebugger_results.md b/yamldebugger_results.md
new file mode 100644
index 0000000..74227d4
--- /dev/null
+++ b/yamldebugger_results.md
@@ -0,0 +1,9 @@
+|Q-Quali |Q folders             |Q Names               |Descriptions stats           |Keywords stats           |Meta Info data fields   |Bad file names                                                                                                                                                             |
+|:-------|:---------------------|:---------------------|:----------------------------|:------------------------|:-----------------------|:--------------------------------------------------------------------------------------------------------------------------------------------------------------------------|
+|C       |MuPoMo_bootstrap      |MuPoMo_bootstrap      |26 word(s), 156 Character(s) |8: 4 (standard), 4 (new) |q, p, a, d, k, e, s, sa |bad Q file names!: Histogram of theta1.png, Prediction intervals at different levels.png                                                                                   |
+|A       |MuPoMo_data           |MuPoMo_data           |21 word(s), 103 Character(s) |6: 3 (standard), 3 (new) |q, p, a, d, k, s, sa    |                                                                                                                                                                           |
+|C       |MuPoMo_main_multipop  |MuPoMo_main_multipop  |26 word(s), 171 Character(s) |7: 3 (standard), 4 (new) |q, p, a, d, k, e, s, sa |bad Q file names!: Multi-Population model with German data.png, Multi-Population model with Japanese data.png                                                              |
+|C       |MuPoMo_main_twopop    |MuPoMo_main_twopop    |34 word(s), 212 Character(s) |8: 4 (standard), 4 (new) |q, p, a, d, k, e, s, sa |bad Q file names!: Contour plot of theta2 and theta4.png, Loss function of theta2.png, Loss surface 3D.png, Model fit and forecast.png, Time shift at different levels.png |
+|A       |MuPoMo_normalization  |MuPoMo_normalization  |18 word(s), 112 Character(s) |5: 4 (standard), 1 (new) |q, p, a, d, k, s, sa    |                                                                                                                                                                           |
+|A       |MuPoMo_optimization   |MuPoMo_optimization   |27 word(s), 131 Character(s) |7: 4 (standard), 3 (new) |q, p, a, d, k, s, sa    |                                                                                                                                                                           |
+|A       |MuPoMo_referencecurve |MuPoMo_referencecurve |23 word(s), 131 Character(s) |5: 4 (standard), 1 (new) |q, p, a, d, k, s, sa    |                                                                                                                                                                           |

From c6ef627da818de0f5362b3b83f547fbff734d1c3 Mon Sep 17 00:00:00 2001
From: Lukas Borke <admin@quantnet.technology>
Date: Fri, 9 Dec 2016 15:01:15 +0100
Subject: [PATCH 28/63] rm md's

---
 MuPoMo_bootstrap/README.md      | 240 --------------------------------
 MuPoMo_data/README.md           |  59 --------
 MuPoMo_main_multipop/README.md  | 192 -------------------------
 MuPoMo_main_twopop/README.md    | 195 --------------------------
 MuPoMo_normalization/README.md  |  50 -------
 MuPoMo_optimization/README.md   | 108 --------------
 MuPoMo_referencecurve/README.md |  51 -------
 7 files changed, 895 deletions(-)
 delete mode 100644 MuPoMo_bootstrap/README.md
 delete mode 100644 MuPoMo_data/README.md
 delete mode 100644 MuPoMo_main_multipop/README.md
 delete mode 100644 MuPoMo_main_twopop/README.md
 delete mode 100644 MuPoMo_normalization/README.md
 delete mode 100644 MuPoMo_optimization/README.md
 delete mode 100644 MuPoMo_referencecurve/README.md

diff --git a/MuPoMo_bootstrap/README.md b/MuPoMo_bootstrap/README.md
deleted file mode 100644
index bdb9f49..0000000
--- a/MuPoMo_bootstrap/README.md
+++ /dev/null
@@ -1,240 +0,0 @@
-
-[<img src="https://github.com/QuantLet/Styleguide-and-FAQ/blob/master/pictures/banner.png" width="880" alt="Visit QuantNet">](http://quantlet.de/index.php?p=info)
-
-## [<img src="https://github.com/QuantLet/Styleguide-and-Validation-procedure/blob/master/pictures/qloqo.png" alt="Visit QuantNet">](http://quantlet.de/) **MuPoMo_bootstrap** [<img src="https://github.com/QuantLet/Styleguide-and-Validation-procedure/blob/master/pictures/QN2.png" width="60" alt="Visit QuantNet 2.0">](http://quantlet.de/d3/ia)
-
-```yaml
-
-Name of QuantLet : MuPoMo_bootstrap
-
-Published in : MuPoMo
-
-Description : 'Forecasts mortality rates based on a semi-parametric approach, and bootstraps time
-series with innovation to compute the prediction intervals. Uses random two countries to
-demonstrate.'
-
-Keywords : 'time series, demography, mortality, population, nonparametric smoothing, parametric
-modelling, Lee-Carter method, bootstrap'
-
-See also : 'MuPoMo_data, MuPoMo_optimization, MuPoMo_normalization, MuPoMo_referencecurve,
-MuPoMo_main_twopop, MuPoMo_main_multipop'
-
-Author : Lei Fang
-
-Submitted : Mon, June 13 2016 by Lei Fang
-
-Example : Prediction intervals at different levels, Histogram of theta1
-
-```
-
-![Picture1](Histogram of theta1.png)
-
-![Picture2](Prediction intervals at different levels.png)
-
-
-### R Code:
-```r
-# clear history and close windows
-rm(list=ls(all=TRUE))
-graphics.off()
-
-# please set working directory
-# setwd("C:/...")     # windows
-# setwd("/Users/...") # mac os
-# setwd("~/...")      # linux
-
-# install packages
-library(demography)
-library(rgl)
-library(sm)
-library(boot)
-library(tseries)
-
-# setting
-par(mar = c(5, 5, 2, 2), cex.axis = 1.5, cex.lab = 2)
-options(digits = 4)
-
-# load saved RData to reduce code-running time from previous procedure (MuPoMo_main_multipop.R)
-# load("~/.../MuPoMo_main_multipop.RData")
-
-# Bootstrap to resample from China's mortality time series to construct the CI for shape deviation parameters theta
-
-# Reference time series curve (unchanged). We use for comparing with resampled Japan's mortality TS
-kt.referencet = reference4
-# Original Japan's mortality TS, from which we are going to take TS bootstrap
-boot.data     = kt.Japan.female
-# Initialize theta values for optimazation
-theta         = theta4[16, ]
-
-### loss function
-loss = function(theta, t, kt, t.reference, kt.reference) {
-    ## assume theta[1]>0, theta[3]>0, if not, take absolute values
-    theta1 = abs(theta[1])
-    theta2 = theta[2]
-    theta3 = abs(theta[3])
-    
-    if (theta[1] < 0 | theta[3] < 0) 
-        warning("theta1 or theta3 <0, abs value is used")
-    # time adjustment
-    sm.t = (t.reference - theta2)/theta3  
-    ## common domain for kt and time-adjusted kt.reference
-    tmin = max(min(t), min(sm.t))
-    tmax = min(max(t), max(sm.t))
-    # index for common domain
-    i0 = which(t >= tmin & t <= tmax)
-    
-    if (length(i0) > 0) {
-        t0 = t[i0]
-        ## smooth interpolation of shifted kt.reference on common grid
-        dref = data.frame(sm.t = sm.t, kt.reference = kt.reference)
-        
-        # sm: sm.regression with optimal smoothing parameter 
-        h.optimal3 = h.select(sm.t, kt.reference) 
-        sm = sm.regression(sm.t, kt.reference, h = h.optimal3, eval.points = t0, model = 'none', poly.index = 1, display = 'none') 
-        mu = theta1 * sm$estimate
-
-        ## mean squared error at common grid points
-        mse = mean((kt[i0] - mu)^2)  # mse of kt and the modelled one
-    } else {
-        mse = 1e+09
-    }
-    return(mse)
-}
-
-# Construct the 'statistic' function which is needed and very important in 'tsboot' tsboot (tseries, statistic, R, l = NULL, sim =
-# 'model',...)
-boot.func = function(kt) {
-    t = time(kt)
-    t.reference = time(kt.reference)
-    ### parameter estimation
-    conv   = 1
-    theta0 = theta
-    while (conv != 0) {
-        # check convergence
-        out    = optim(theta0, loss, gr = NULL, t, kt, t.reference, kt.reference, control = list(maxit = 1000))  # optimization
-        conv   = out$convergence
-        theta0 = out$par
-    }
-    # add constraint on theta2
-    if (out$par[2] >= -200 & out$par[2] <= 200) 
-        temp.par = out$par else temp.par = theta
-    result = c(temp.par, out$value, out$convergence)
-}
-
-# simulate time series with innovation
-bootdata.fit = auto.arima(boot.data)
-sim = 500
-plot(boot.data, xlab = "Time", ylab = "Kt", ylim = c(-150, 70), col = "blue", lwd = 10)
-
-for (i in 1:sim) {
-    nam5  = paste("sim.ts", i, sep = ".")
-    # simulate time seriese based on bootstrap of innovation/error term in ARIMA fitting model
-    temp5 = simulate(bootdata.fit, nsim = length(boot.data), future = FALSE, bootstrap = TRUE)
-    assign(nam5, temp5)
-    # time series test on plot
-    lines(temp5, col = "grey")
-}
-
-# compute parameters theta's based on bootstrapped time series
-theta.boot = matrix(rep(c(0, 0, 0, 0, 0), sim), sim, 5, byrow = TRUE)
-
-for (i in 1:sim) {
-    theta.boot[i, ] = boot.func(eval(parse(text = paste("sim.ts", i, sep = "."))))
-}
-
-# plot test
-hist(theta.boot[, 1], xlab = "theta 1", main = "Histogram of theta 1")
-quantile(theta.boot[, 1])
-
-hist(theta.boot[, 2][which(theta.boot[, 2] >= -100 & theta.boot[, 2] <= 100)], xlab = "theta 2", 
-     main = "Histogram of theta 2", xlim = c(-5, 5), breaks = 10)
-quantile(theta.boot[, 2])
-
-hist(theta.boot[, 3][which(theta.boot[, 3] >= 0.8 & theta.boot[, 3] <= 1.2)], xlab = "theta 3", 
-     main = "Histogram of theta 3", xlim = c(0.93, 0.99), breaks = 10)
-quantile(theta.boot[, 3])
-
-# forecast with estimated parameters from bootstrap
-boot.forecast = function(theta, kt, kt.reference) {
-    t = time(kt)
-    t.reference = time(kt.reference)
-    ### check results on graph
-    theta1 = abs(theta[1])
-    theta2 = theta[2]
-    theta3 = abs(theta[3])
-    # time adjustment
-    sm.t = (t.reference - theta2)/theta3
-    ## common grid for kt and shifted kt.reference
-    tmin = max(min(t), min(sm.t))
-    tmax = min(max(t), max(sm.t))
-    i0   = which(t >= tmin & t <= tmax)
-    t0   = t[i0]
-    ## shifted curves (kt.hat)
-    dref = data.frame(sm.t = sm.t, kt.reference = kt.reference)
-    # sm: sm.regression with optimal smoothing parameter
-    h.optimal4 = h.select(sm.t, kt.reference)
-    sm = sm.regression(sm.t, kt.reference, h = h.optimal4, eval.points = sm.t, model = "none", poly.index = 1, display = "none")
-    mu = theta1 * sm$estimate
-
-    mu = ts(mu, start = sm.t[1], frequency = theta3)
-    
-    # sm: sm.regression with optimal smoothing parameter
-    h.optimal5 = h.select(sm.t, kt.reference)
-    sm0 = sm.regression(sm.t, kt.reference, h = h.optimal5, eval.points = t0, model = "none", poly.index = 1, display = "none")
-    mu0 = theta1 * sm0$estimate
-
-    mu0 = ts(mu0, start = t0[1], frequency = 1)
-    
-    return(list(mu, mu0, tmin, tmax))
-}
-
-# forecast
-plot(forecast(bootdata.fit, h = 40, level = 95), xlab = "Time", ylab = "Kt", xlim = c(1828, 2050), ylim = c(-200, 150))
-lines(kt.referencet, col = "blue", lwd = 5)
-lines(boot.data, col = "red", lwd = 5)
-
-for (i in 1:sim) {
-    temp  = boot.forecast(theta.boot[i, 1:3], boot.data, kt.reference)
-    nam12 = paste("shift.kt.boot", i, sep = ".")
-    assign(nam12, temp[[2]])
-    nam15 = paste("mu.boot", i, sep = ".")
-    assign(nam15, temp[[1]])
-    lines(temp[[2]], col = "green")  
-    lines(temp[[1]], col = "grey")  
-}
-
-# prediction interval
-for (i in 2010:2050) {
-    nam = matrix(0, 1, 500)
-    for (j in 1:sim) {
-        if (max(time(eval(parse(text = paste("mu.boot", j, sep = "."))))) >= i) 
-            nam[j] = window(eval(parse(text = paste("mu.boot", j, sep = "."))), i)[1] else nam[j] = NA
-    }
-    nam1 = paste("ts", i, sep = ".")
-    assign(nam1, nam)
-    nam2 = paste("ts", i, 5, sep = ".")
-    assign(nam2, quantile(nam, probs = seq(0, 1, 0.05), na.rm = T)[2])
-    nam3 = paste("ts", i, 95, sep = ".")
-    assign(nam3, quantile(nam, probs = seq(0, 1, 0.05), na.rm = T)[20])
-    nam4 = paste("ts", i, 20, sep = ".")
-    assign(nam4, quantile(nam, probs = seq(0, 1, 0.05), na.rm = T)[5])
-    nam5 = paste("ts", i, 80, sep = ".")
-    assign(nam5, quantile(nam, probs = seq(0, 1, 0.05), na.rm = T)[17])
-}
-
-for (j in c(5, 20, 80, 95)) {
-    ts.temp = ts(0, start = 2010, end = 2040, frequency = 1)
-    for (i in 2010:2040) {
-        ts.temp[i - 2009] = eval(parse(text = paste("ts", i, j, sep = ".")))
-    }
-    nam6 = paste("ts.forecast", j, sep = ".")
-    assign(nam6, ts.temp)
-}
-
-# plot
-plot(boot.data, lwd = 5, xlab = "Time", ylab = "Kt", xlim = c(1828, 2050), ylim = c(-200, 150))
-polygon(c(2010:2040, rev(2010:2040)), c(ts.forecast.5, rev(ts.forecast.95)), col = "yellow", border = FALSE)
-polygon(c(2010:2040, rev(2010:2040)), c(ts.forecast.20, rev(ts.forecast.80)), col = "Gray", border = FALSE)
-lines(kt.referencet, col = "blue", lwd = 5)
-lines(mu.China.4, col = 5, lty = 2, lwd = 4)
-```
diff --git a/MuPoMo_data/README.md b/MuPoMo_data/README.md
deleted file mode 100644
index 94fea62..0000000
--- a/MuPoMo_data/README.md
+++ /dev/null
@@ -1,59 +0,0 @@
-
-[<img src="https://github.com/QuantLet/Styleguide-and-FAQ/blob/master/pictures/banner.png" width="880" alt="Visit QuantNet">](http://quantlet.de/index.php?p=info)
-
-## [<img src="https://github.com/QuantLet/Styleguide-and-Validation-procedure/blob/master/pictures/qloqo.png" alt="Visit QuantNet">](http://quantlet.de/) **MuPoMo_data** [<img src="https://github.com/QuantLet/Styleguide-and-Validation-procedure/blob/master/pictures/QN2.png" width="60" alt="Visit QuantNet 2.0">](http://quantlet.de/d3/ia)
-
-```yaml
-
-Name of QuantLet : MuPoMo_data
-
-Published in : MuPoMo
-
-Description : 'Reads data from Human Mortality Database and calculate kt, and will be called in
-MuPoMo_main_twopop and MuPoMo_main_multipop.'
-
-Keywords : 'time series, demography, mortality, Lee-Carter method, population, Human Mortality
-Database'
-
-See also : 'MuPoMo_optimization, MuPoMo_normalization, MuPoMo_referencecurve, MuPoMo_main_twopop,
-MuPoMo_main_multipop, MuPoMo_bootstrap'
-
-Author : Lei Fang
-
-Submitted : Mon, June 13 2016 by Lei Fang
-
-```
-
-
-### R Code:
-```r
-# read multi-pop female mortality rates from Human Mortality Database
-shortnames.all = c("AUS", "AUT", "BLR", "BGR", "CAN", "CHL", "CZE", "DNK", "EST", "FIN", "FRATNP", "DEUTNP", "HUN", "ISL", "IRL", 
-    "ISR", "ITA", "JPN", "LVA", "LTU", "LUX", "NLD", "NZL_NP", "NOR", "POL", "PRT", "RUS", "SVK", "SVN", "ESP", "CHE", "TWN", "GBR_NP", 
-    "USA", "SWE")
-names.all = c("Australia", "Austria", "Belarus", "Bulgaria", "Canada", "Chile", "CzechRepublic", "Denmark", "Estonia", "Finland", 
-    "France", "Germany", "Hungary", "Iceland", "Ireland", "Israel", "Italy", "Japan", "Latvia", "Lithuania", "Luxembourg", "Netherlands", 
-    "NewZealand", "Norway", "Poland", "Portugal", "Russia", "Slovakia", "Slovenia", "Spain", "Switzerland", "Taiwan", "UnitedKingdom", 
-    "USA", "Sweden")
-
-loop.all = length(names.all)
-for (i in 1:loop.all) {
-    nam1 = paste(names.all[i])
-    # read data from Human Mortality Database (HMD: http://www.mortality.org/)
-    # you need register on HMD to access a free account accound and set up your password
-    assign(nam1, hmd.mx(shortnames.all[i], "account", "password", names.all[i]))
-    temp1 = hmd.mx(shortnames.all[i], "account", "password", names.all[i])
-    nam2  = paste(names.all[i], "lca.female", sep = ".")
-    # Lee-Carter method
-    assign(nam2, lca(temp1, series = "female", adjust = "dt", interpolate = TRUE))
-    temp2 = lca(temp1, series = "female", adjust = "dt", interpolate = TRUE)
-    nam3  = paste("ax", names.all[i], "female", sep = ".")  # ax
-    assign(nam3, temp2$ax)
-    nam4  = paste("bx", names.all[i], "female", sep = ".")  # bx
-    assign(nam4, temp2$bx)
-    nam5  = paste("kt", names.all[i], "female", sep = ".")  # kt
-    assign(nam5, temp2$kt)
-}
-
-
-```
diff --git a/MuPoMo_main_multipop/README.md b/MuPoMo_main_multipop/README.md
deleted file mode 100644
index baccb3e..0000000
--- a/MuPoMo_main_multipop/README.md
+++ /dev/null
@@ -1,192 +0,0 @@
-
-[<img src="https://github.com/QuantLet/Styleguide-and-FAQ/blob/master/pictures/banner.png" width="880" alt="Visit QuantNet">](http://quantlet.de/index.php?p=info)
-
-## [<img src="https://github.com/QuantLet/Styleguide-and-Validation-procedure/blob/master/pictures/qloqo.png" alt="Visit QuantNet">](http://quantlet.de/) **MuPoMo_main_multipop** [<img src="https://github.com/QuantLet/Styleguide-and-Validation-procedure/blob/master/pictures/QN2.png" width="60" alt="Visit QuantNet 2.0">](http://quantlet.de/d3/ia)
-
-```yaml
-
-Name of QuantLet : MuPoMo_main_multipop
-
-Published in : MuPoMo
-
-Description : 'Estimates and forecasts mortality rates based on a semi-parametric approach, which
-applies parametric modelling for multiple nonparametric smoothed curves with the shape-related
-nonlinear variation.'
-
-Keywords : 'time series, demography, mortality, population, nonparametric smoothing, parametric
-modelling, Lee-Carter method'
-
-See also : 'MuPoMo_data, MuPoMo_optimization, MuPoMo_normalization, MuPoMo_referencecurve,
-MuPoMo_main_twopop, MuPoMo_bootstrap'
-
-Author : Lei Fang
-
-Submitted : Mon, June 13 2016 by Lei Fang
-
-Example : Multi-Population model with German data, Multi-Population model with Japanese data
-
-```
-
-![Picture1](Multi-Population model with German data.png)
-
-![Picture2](Multi-Population model with Japanese data.png)
-
-
-### R Code:
-```r
-# clear history and close windows
-rm(list=ls(all=TRUE))
-graphics.off()
-
-# please set working directory
-# setwd("C:/...")     # windows
-# setwd("/Users/...") # mac os
-# setwd("~/...")      # linux
-
-# install packages
-library(demography)
-library(rgl)
-library(sm)
-
-# set plot
-par(mar = c(5, 5, 2, 2), cex.axis = 1.5, cex.lab = 2)
-
-# recall self-defined functions
-source('MuPoMo_data.R')
-source("MuPoMo_optimization.R")
-source("MuPoMo_normalization.R")
-source("MuPoMo_referencecurve.R")
-
-# set bandwidth
-bw.default = 2.5
-
-## descriptive plot plot kt of 35 countries
-plot(kt.Sweden.female, type = "l", ylim = c(-250, 150), xlab = "Time", ylab = "kt", main = "Original Kt (35 countries)")
-for (i in 1:(loop.all - 1)) {
-    lines(eval(parse(text  = paste("kt.", names.all[i], ".female", sep = ""))), col = i)
-}
-
-##### common trend
-#### initial setting nonparametric smoothing 35 countries
-for (i in 1:loop.all) {
-    kt = eval(parse(text = paste("kt.", names.all[i], ".female", sep = "")))
-    t  = eval(parse(text = paste(names.all[i])))$year
-    d  = data.frame(kt, t)
-    # sm: sm.regression with optimal smoothing parameter
-    h.optimal1 = h.select(t, kt)
-    sm         = sm.regression(t, kt, h = h.optimal1, eval.points = t, model = "none", poly.index = 1, display = "none")
-    nam6       = paste("sm.kt", names.all[i], "female", sep = ".")
-    temp6      = ts(sm$estimate, start = t[1], frequency = 1)
-    assign(nam6, temp6)
-}
-
-## plot smoothed kt of 35 countries
-plot(sm.kt.Sweden.female, type = "l", ylim = c(-250, 150), xlab = "Time", ylab = "kt", main = "Smoothed Kt (35 countries)")
-for (i in 1:(loop.all - 1)) {
-    lines(eval(parse(text = paste("sm.kt.", names.all[i], ".female", sep = ""))), col = i)
-}
-
-#### intial values of thetas 
-### remove Russia, Lithuavia, Latvia, Estonia and Belarus 
-### set up the initial reference curve based on 31 countries
-names.31 = c("Australia", "Austria", "Bulgaria", "Canada", "Chile", "CzechRepublic", "Denmark", "Finland", "France", "Germany", "Hungary", 
-    "Iceland", "Ireland", "Israel", "Italy", "Japan", "Luxembourg", "Netherlands", "NewZealand", "Norway", "Poland", "Portugal", "Slovakia", 
-    "Slovenia", "Spain", "Switzerland", "Taiwan", "UnitedKingdom", "USA", "Sweden")
-loop.31  = length(names.31)
-merge1   = sm.kt.Australia.female
-for (i in 1:(loop.31 - 1)) {
-    nam7  = paste("merge", i + 1, sep = "")
-    temp3 = merge.zoo(eval(parse(text = paste("merge", i, sep = ""))), eval(parse(text = paste("sm.kt.", names.31[i + 1], ".female", 
-        sep = ""))))
-    assign(nam7, temp3)
-}
-reference0.temp = rowMeans(merge31, na.rm = TRUE)
-reference0      = ts(reference0.temp, start = Sweden$year[1], frequency = 1)
-
-## plot the reference curve among all 31 smoothed curves
-plot(sm.kt.Sweden.female, type = "l", ylim = c(-250, 150), xlab = "Time", ylab = "kt", main = "Reference Curve vs. Smoothed Kt (31 countries)")
-for (i in 1:loop.31) {
-    lines(eval(parse(text = paste("sm.kt.", names.31[i], ".female", sep = ""))), col = i)
-}
-lines(reference0, lwd = 4, col = "red")
-
-##### begin loop
-theta0    = matrix(rep(c(1, 0, 1), loop.31), loop.31, 3, byrow = TRUE)
-iteration = 5
-for (j in 1:iteration) {
-    ### find the optimal initial theta based on the reference curve
-    theta        = eval(parse(text = paste("theta", j - 1, sep = "")))
-    kt.reference = eval(parse(text = paste("reference", j - 1, sep = "")))
-    results      = matrix(NA, loop.31, 5)  # c(theta1,theta2,theta3, loss, convergence)
-    for (i in 1:loop.31) {
-        kt           = eval(parse(text = paste("sm.kt.", names.31[i], ".female", sep = "")))
-        tt           = time(kt)
-        ltt          = length(tt)
-        temp4        = optimization(theta[i, ], kt, kt.reference)
-        results[i, ] = temp4[[1]]
-        nam12        = paste("shift.kt", names.31[i], j, sep = ".")
-        assign(nam12, temp4[[3]])
-        nam15        = paste("mu", names.31[i], j, sep = ".")
-        assign(nam15, temp4[[2]])
-        pdf(paste("plot_", j, "_", i, ".pdf", sep = ""))
-        par(mar = c(5, 5, 2, 2))
-        plot(eval(parse(text = paste("kt.", names.31[i], ".female", sep = ""))), ylim = c(-250, 150), xlim = c(1750, 2020), type = "p", 
-            xlab = "Time", ylab = "kt", main = paste(names.31[i], tt[1], "--", tt[ltt], ":step", j))
-        lines(kt, col = 2)  # sm.kt
-        lines(kt.reference, col = 4, lwd = 2)  # reference
-        lines(temp4[[2]], col = 5, lty = 5)  # new kt
-        lines(temp4[[3]], col = 5, lwd = 2)  # new kt
-        abline(v = temp4[[4]], col = "gray", lty = 5)
-        abline(v = temp4[[5]], col = "gray", lty = 5)
-        # legend('topright', legend=c('kt', 'sm.kt', 'k0', 'kt.hat'), col=c(1,2,4,5), lty=1)
-        dev.off()
-    }
-    nam16 = paste("results", j, sep = "")
-    assign(nam16, results)
-    nam18 = paste("theta", j, sep = "")
-    assign(nam18, results[, 1:3])
-    
-    ## plot shifted kt of 31 countries and the reference curve of previous step
-    plot(kt.reference, type = "l", ylim = c(-250, 150), xlab = "Time", ylab = "kt", lwd = 4, col = "red", main = paste("Reference Curve vs. Shifted Kt (31 countries): step", 
-        j - 1))
-    for (i in 1:loop.31) {
-        lines(eval(parse(text = paste("shift.kt", names.31[i], j, sep = "."))), col = i)
-    }
-    
-    # construct optimal.theta.matrix and normalize optimal theta
-    optimal.theta.matrix          = results[, 1:3]
-    standard.optimal.theta.matrix = normalization(optimal.theta.matrix)
-    
-    # construct new reference curve
-    for (i in 1:loop.31) {
-        nam13 = paste("shift.kt", names.31[i], "standard", sep = ".")
-        assign(nam13, referencecurve(standard.optimal.theta.matrix[i, 2], standard.optimal.theta.matrix[i, 3], eval(parse(text = paste("sm.kt.", 
-            names.31[i], ".female", sep = ""))), eval(parse(text = paste("shift.kt", names.31[i], j, sep = ".")))))
-    }
-    merge1.1  = shift.kt.Australia.standard
-    for (i in 1:(loop.31 - 1)) {
-        nam7  = paste("merge1", i + 1, sep = ".")
-        temp3 = merge.zoo(eval(parse(text = paste("merge1", i, sep = "."))), eval(parse(text = paste("shift.kt", names.31[i + 1], 
-            "standard", sep = "."))))
-        assign(nam7, temp3)
-    }
-    reference.temp           = rowMeans(merge1.31, na.rm = TRUE)
-    reference.temp.nonsmooth = ts(reference.temp, start = min(index(merge1.31)), frequency = 1)
-    t.temp                   = time(reference.temp.nonsmooth)
-    
-    ## smooth the updated reference curve
-    # sm: sm.regression
-    temp17 = sm.regression(t.temp, reference.temp.nonsmooth, eval.points = t.temp, model = "none", poly.index = 1, display = "none")
-    nam17  = paste("reference", j, sep = "")
-    assign(nam17, ts(temp17$estimate, start = t.temp[1], frequency = 1))
-    
-    ## plot the updated reference curve among all 31 shifted curves
-    plot(eval(parse(text = paste("reference", j, sep = ""))), lwd = 4, col = "red", type = "l", ylim = c(-250, 150), xlab = "Time", 
-        ylab = "kt", main = paste("Updated Reference Curve vs. Shifted Kt (31 countries): step", j))
-    for (i in 1:loop.31) {
-        lines(eval(parse(text = paste("shift.kt", names.31[i], j, sep = "."))), col = i)
-        lines(eval(parse(text = paste("sm.kt.", names.31[i], ".female", sep = ""))), col = "grey")
-    }
-    lines(eval(parse(text = paste("reference", j - 1, sep = ""))), col = "blue", lwd = 3, lty = 5)
-}
-```
diff --git a/MuPoMo_main_twopop/README.md b/MuPoMo_main_twopop/README.md
deleted file mode 100644
index 74e74bb..0000000
--- a/MuPoMo_main_twopop/README.md
+++ /dev/null
@@ -1,195 +0,0 @@
-
-[<img src="https://github.com/QuantLet/Styleguide-and-FAQ/blob/master/pictures/banner.png" width="880" alt="Visit QuantNet">](http://quantlet.de/index.php?p=info)
-
-## [<img src="https://github.com/QuantLet/Styleguide-and-Validation-procedure/blob/master/pictures/qloqo.png" alt="Visit QuantNet">](http://quantlet.de/) **MuPoMo_main_twopop** [<img src="https://github.com/QuantLet/Styleguide-and-Validation-procedure/blob/master/pictures/QN2.png" width="60" alt="Visit QuantNet 2.0">](http://quantlet.de/d3/ia)
-
-```yaml
-
-Name of QuantLet : MuPoMo_main_twopop
-
-Published in : MuPoMo
-
-Description : 'Estimates and forecasts mortality rates based on a semi-parametric approach, which
-applies parametric modelling for multiple nonparametric curves with the shape-related nonlinear
-variation. Uses random two countries to demonstrate two-country case.'
-
-Keywords : 'time series, demography, mortality, population, nonparametric smoothing, parametric
-modelling, Lee-Carter method, contour'
-
-See also : 'MuPoMo_data, MuPoMo_optimization, MuPoMo_normalization, MuPoMo_referencecurve,
-MuPoMo_main_multipop, MuPoMo_bootstrap'
-
-Author : Lei Fang
-
-Submitted : Mon, June 13 2016 by Lei Fang
-
-Example : 'Time shift at different levels, Loss function of theta2, Loss surface 3D, Contour plot
-of theta2 and theta4, Model fit and forecast'
-
-```
-
-![Picture1](Contour plot of theta2 and theta4.png)
-
-![Picture2](Loss function of theta2.png)
-
-![Picture3](Loss surface 3D.png)
-
-![Picture4](Model fit and forecast.png)
-
-![Picture5](Time shift at different levels.png)
-
-
-### R Code:
-```r
-# clear history and close windows
-rm(list=ls(all=TRUE))
-graphics.off()
-
-# please set working directory
-# setwd("C:/...")     # windows
-# setwd("/Users/...") # mac os
-# setwd("~/...")      # linux
-
-# install packages
-library(demography)
-library(rgl)
-library(sm)
-
-# set plot
-par(mar = c(5, 5, 2, 2), cex.axis = 1.5, cex.lab = 2)
-
-# recall self-defined functions
-# read data and compute kt based on Lee-Carter Model via source('data.R')
-source('MuPoMo_data.R')
-source("MuPoMo_optimization.R")
-
-# choose two countries' kt for this analysis
-kt1 = kt.China.female
-kt2 = kt.Japan.female
-
-# set bandwidth for smoothing curves
-bw.default     = 2.5
-
-# plot kt
-plot(kt2, type = "l", col = "blue", lwd = 4, xlab = "Time", ylab = "Kt")
-lines(kt1, col = "red", lwd = 4)
-
-# shift movement of the two smoothed countries
-t1         = 1994:2010 # differ based on the chosen country
-d1         = data.frame(time(kt1), kt1)
-h.optimal1 = h.select(time(kt1), kt1)
-sm1        = sm.regression(time(kt1), kt1, h = h.optimal1, eval.points = time(kt1), model = "none", poly.index = 1, display = "none")
-sm.kt1     = sm1$estimate  # smoothed kt1
-
-t2         = 1947:2012 # differ based on the chosen country
-d2         = data.frame(time(kt2), kt2)
-h.optimal2 = h.select(time(kt2), kt2)
-sm2        = sm.regression(time(kt2), kt2, h = h.optimal2, eval.points = time(kt2), model = "none", poly.index = 1, display = "none")
-sm.kt2     = sm2$estimate  # smoothed kt2
-
-plot(t2, sm.kt2, type = "l", col = "blue", lwd = 4, xlab = "Time", ylab = "Kt")
-lines(kt2, col = "red", lwd = 4)
-lines(t1, sm.kt1, lwd = 4)
-lines(kt1, col = "darkgreen", lwd = 4)
-lines(t2 + 20, sm.kt2, lwd = 4, lty = 2) # differ based on the chosen country
-lines(t2 + 25, sm.kt2, lwd = 4, lty = 3)
-lines(t2 + 30, sm.kt2, lwd = 4, lty = 4)
-
-# time delay
-plot(t2, sm.kt2, type = "l", col = "blue", lwd = 4, xlab = "Time", ylab = "Kt")
-lines(t1, sm.kt1, lwd = 4)
-lines(t2 + 23, sm.kt2, lwd = 4, lty = 4, col = "blue") # differ based on the chosen country
-
-# vertical shift
-plot(t2, sm.kt2, type = "l", col = "blue", lwd = 4, xlab = "Time", ylab = "Kt")
-lines(t1, sm.kt1, lwd = 4)
-lines(t2, sm.kt2 + 85, lwd = 4, lty = 4, col = "blue") # differ based on the chosen country
-
-# optimization
-theta.2pop  = c(1, -23, 1) # differ based on the chosen country
-result.2pop = optimization(theta.2pop, kt1, kt2)
-
-# plot optimized movement
-plot(t2, sm.kt2, type = "l", col = 4, lwd = 4, xlab = "Time", ylab = "Kt")
-lines(kt2, type = "p", lwd = 3)
-lines(t1, sm.kt1, lwd = 4, col = 2)
-lines(kt1, type = "p", lwd = 3)
-lines(result.2pop[[2]], col = 5, lty = 5)  #
-lines(result.2pop[[3]], col = 5, lwd = 3)  #
-abline(v = result.2pop[[4]], col = "gray", lty = 5)
-abline(v = result.2pop[[5]], col = "gray", lty = 5)
-
-# plot loss function
-loss = function(theta1, theta2, theta3, theta4, t, kt, t.reference, kt.reference) {
-    sm.t = (t.reference - theta2)/theta3  # time adjustment
-    ## common domain for kt and time-adjusted kt.reference
-    tmin = max(min(t), min(sm.t))
-    tmax = min(max(t), max(sm.t))
-    i0 = which(t >= tmin & t <= tmax)  # index for common domain
-    if (length(i0) > 0) {
-        t0 = t[i0]
-        ## smooth interpolation of shifted kt.reference on common grid
-        dref = data.frame(sm.t = sm.t, kt.reference = kt.reference)
-        # sm: sm.regression with optimal smoothing parameter
-        h.optimal3 = h.select(sm.t, kt.reference)
-        sm = sm.regression(sm.t, kt.reference, h = h.optimal3, eval.points = t0, model = "none", poly.index = 1, display = "none")
-        mu = theta1 * sm$estimate + theta4
-        ## mean squared error at common grid points
-        mse = mean((kt[i0] - mu)^2)  # mse of kt and the modelled one
-    } else {
-        mse = 1e+09
-    }
-    return(mse)
-}
-
-# plot loss function of theta2 and theta4
-vtheta2 = seq(-30, 10, len = 100) # differ based on the chosen country
-vtheta4 = seq(0, 100, len = 100) # differ based on the chosen country
-npar    = length(vtheta2)
-res     = matrix(rep(0, 10000), 100, 100)
-for (i in 1:npar) {
-    for (l in 1:npar) {
-        res[i, l] = loss(1, vtheta2[i], 1, vtheta4[l], t1, kt1, t2, kt2)
-    }
-    res[i, l] = loss(1, vtheta2[i], 1, vtheta4[l], t1, kt1, t2, kt2)
-}
-
-persp3d(vtheta2, vtheta4, res, col = "blue", xlab = "theta2", ylab = "theta4", zlab = "Loss")
-
-resnew = res * (res < 5000)
-persp3d(vtheta2, vtheta4, resnew, col = "blue", xlab = "theta2", ylab = "theta4", zlab = "Loss")
-
-# contour plot
-contour(vtheta2, vtheta4, resnew, col = rainbow(20), nlevels = 20, lwd = 1, xlim = c(-23, 0), ylim = c(0, 80))
-contour(vtheta2, vtheta4, res, col = rainbow(20), nlevels = 70, lwd = 1, xlim = c(-23, 0), ylim = c(0, 80), zlim = c(0, 100))
-contour(vtheta2, vtheta4, res, col = rainbow(20), nlevels = 70, lwd = 1, xlim = c(-10, -2), ylim = c(40, 80), zlim = c(0, 100))
-
-# plot loss function of theta2
-vtheta22 = seq(-50, 0, len = 100) # differ based on the chosen country
-npar2    = length(vtheta22)
-res2     = rep(0, 100)
-for (i in 1:npar2) {
-    res2[i] = loss(1, vtheta22[i], 1, 0, t1, kt1, t2, kt2)
-}
-plot(vtheta22, res2, col = "blue", xlab = "theta2", ylab = "Loss", type = "l", lwd = 4)
-
-# plot loss function of theta4
-vtheta42 = seq(40, 140, len = 100) # differ based on the chosen country
-npar3    = length(vtheta42)
-res3     = rep(0, 100)
-for (i in 1:npar3) {
-    res3[i] = loss(1, 0, 1, vtheta42[i], t1, kt1, t2, kt2)
-}
-plot(vtheta42, res3, col = "blue", xlab = "theta4", ylab = "Loss", type = "l", lwd = 4)
-
-# forecast
-plot(t2, sm.kt2, type = "l", col = 4, lwd = 4, xlab = "Time", ylab = "Kt", xlim = c(1947, 2035))
-lines(kt2, type = "p", lwd = 3)
-lines(t1, sm.kt1, lwd = 4, col = 2)
-lines(kt1, type = "p", lwd = 3)
-lines(result.2pop[[2]], col = 4, lty = 5, lwd = 3)  #
-lines(result.2pop[[3]], col = "purple", lwd = 3)  #
-abline(v = result.2pop[[4]], col = "gray", lty = 5)
-abline(v = result.2pop[[5]], col = "gray", lty = 5)
-
-```
diff --git a/MuPoMo_normalization/README.md b/MuPoMo_normalization/README.md
deleted file mode 100644
index 0751111..0000000
--- a/MuPoMo_normalization/README.md
+++ /dev/null
@@ -1,50 +0,0 @@
-
-[<img src="https://github.com/QuantLet/Styleguide-and-FAQ/blob/master/pictures/banner.png" width="880" alt="Visit QuantNet">](http://quantlet.de/index.php?p=info)
-
-## [<img src="https://github.com/QuantLet/Styleguide-and-Validation-procedure/blob/master/pictures/qloqo.png" alt="Visit QuantNet">](http://quantlet.de/) **MuPoMo_normalization** [<img src="https://github.com/QuantLet/Styleguide-and-Validation-procedure/blob/master/pictures/QN2.png" width="60" alt="Visit QuantNet 2.0">](http://quantlet.de/d3/ia)
-
-```yaml
-
-Name of QuantLet : MuPoMo_normalization
-
-Published in : MuPoMo
-
-Description : 'Normalizes optimal shape variation parameters theta estimated from
-MuPoMo_optimization, and will be called in MuPoMo_main_multipop.'
-
-Keywords : time series, demography, mortality, population, normalization
-
-See also : 'MuPoMo_data, MuPoMo_optimization, MuPoMo_referencecurve, MuPoMo_main_twopop,
-MuPoMo_main_multipop, MuPoMo_bootstrap'
-
-Author : Lei Fang
-
-Submitted : Mon, June 13 2016 by Lei Fang
-
-```
-
-
-### R Code:
-```r
-normalization  = function(theta) {
-    theta.temp = colSums(theta)
-    for (i in 1:loop.31) {
-        nam10  = paste("normal.theta", names.31[i], 1, sep = ".")
-        assign(nam10, loop.31 * theta[i, 1]/theta.temp[1])
-        nam11  = paste("normal.theta", names.31[i], 3, sep = ".")
-        assign(nam11, loop.31 * theta[i, 3]/theta.temp[3])
-        nam12  = paste("normal.theta", names.31[i], 2, sep = ".")
-        assign(nam12, theta[i, 2] - theta.temp[2]/loop.31)
-        nam14  = paste("normal.theta", names.31[i], sep = ".")
-        assign(nam14, c(eval(parse(text = paste("normal.theta", names.31[i], 1, sep = "."))), eval(parse(text = paste("normal.theta", 
-            names.31[i], 2, sep = "."))), eval(parse(text = paste("normal.theta", names.31[i], 3, sep = ".")))))
-    }
-    ll = list()
-    for (i in 1:loop.31) {
-        ll[[i]]  = c(eval(parse(text = paste("normal.theta", names.31[i], sep = "."))))
-    }
-    normal.theta = do.call(rbind, ll)
-    return(normal.theta)
-}
-
-```
diff --git a/MuPoMo_optimization/README.md b/MuPoMo_optimization/README.md
deleted file mode 100644
index 77ce1b8..0000000
--- a/MuPoMo_optimization/README.md
+++ /dev/null
@@ -1,108 +0,0 @@
-
-[<img src="https://github.com/QuantLet/Styleguide-and-FAQ/blob/master/pictures/banner.png" width="880" alt="Visit QuantNet">](http://quantlet.de/index.php?p=info)
-
-## [<img src="https://github.com/QuantLet/Styleguide-and-Validation-procedure/blob/master/pictures/qloqo.png" alt="Visit QuantNet">](http://quantlet.de/) **MuPoMo_optimization** [<img src="https://github.com/QuantLet/Styleguide-and-Validation-procedure/blob/master/pictures/QN2.png" width="60" alt="Visit QuantNet 2.0">](http://quantlet.de/d3/ia)
-
-```yaml
-
-Name of QuantLet : MuPoMo_optimization
-
-Published in : MuPoMo
-
-Description : 'Optimizes shape variation parameters theta based on kt and reference curve to update
-new kt, and will be called in MuPoMo_main_twopop and MuPoMo_main_multipop.'
-
-Keywords : 'time series, demography, mortality, population, nonlinear, optimization, non parametric
-smoothing'
-
-See also : 'MuPoMo_data, MuPoMo_normalization, MuPoMo_referencecurve, MuPoMo_main_twopop,
-MuPoMo_main_multipop, MuPoMo_bootstrap'
-
-Author : Lei Fang, Juhyun Park
-
-Submitted : Mon, June 13 2016 by Lei Fang
-
-```
-
-
-### R Code:
-```r
-optimization = function(theta, kt, kt.reference) {
-           t = time(kt)
- t.reference = time(kt.reference)
-    
-    ### loss function
-    loss = function(theta, t, kt, t.reference, kt.reference) {
-        ## assume theta[1]>0, theta[3]>0, if not, take absolute values
-        theta1 = abs(theta[1])
-        theta2 = theta[2]
-        theta3 = abs(theta[3])
-        
-        if (theta[1] < 0 | theta[3] < 0) 
-            warning("theta1 or theta3 <0, abs value is used")
-        sm.t = (t.reference - theta2)/theta3  # time adjustment
-        ## common domain for kt and time-adjusted kt.reference
-        tmin = max(min(t), min(sm.t))
-        tmax = min(max(t), max(sm.t))
-        i0   = which(t >= tmin & t <= tmax)  # index for common domain
-        if (length(i0) > 0) {
-            t0 = t[i0]
-            ## smooth interpolation of shifted kt.reference on common grid
-            dref = data.frame(sm.t = sm.t, kt.reference = kt.reference)
-            # sm: sm.regression with optimal smoothing parameter
-            h.optimal3 = h.select(sm.t, kt.reference)
-            sm = sm.regression(sm.t, kt.reference, h = h.optimal3, eval.points = t0, model = "none", poly.index = 1, display = "none")
-            mu = theta1 * sm$estimate
-            ## mean squared error at common grid points
-            mse = mean((kt[i0] - mu)^2)  # mse of kt and the modelled one
-        } else {
-            mse = 1e+09
-        }
-        return(mse)
-    }
-    
-    ### parameter estimation with nonlinear optimization
-    conv   = 1
-    theta0 = theta
-    while (conv != 0) {
-        # check convergence
-        out    = optim(theta0, loss, gr = NULL, t, kt, t.reference, kt.reference, control = list(maxit = 1000))  # optimization
-        conv   = out$convergence
-        theta0 = out$par
-    }
-    ### constraint on theta2 (time shift parameter)
-    if (out$par[2] >= -200 & out$par[2] <= 200) 
-        temp.par = out$par else temp.par = theta
-    result = c(temp.par, out$value, out$convergence)
-    
-    ### check results on graph
-    theta  = result[1:3]
-    theta1 = abs(theta[1])
-    theta2 = theta[2]
-    theta3 = abs(theta[3])
-    
-    sm.t   = (t.reference - theta2)/theta3  # time adjustment
-    ## common grid for kt and shifted kt.reference
-    tmin   = max(min(t), min(sm.t))
-    tmax   = min(max(t), max(sm.t))
-    i0     = which(t >= tmin & t <= tmax)
-    t0     = t[i0]
-    ## shifted curves (kt.hat)
-    dref   = data.frame(sm.t = sm.t, kt.reference = kt.reference)
-    
-    # sm: sm.regression with optimal smoothing parameter
-    h.optimal4 = h.select(sm.t, kt.reference)
-    sm         = sm.regression(sm.t, kt.reference, h = h.optimal4, eval.points = sm.t, model = "none", poly.index = 1, display = "none")
-    mu         = theta1 * sm$estimate
-    mu         = ts(mu, start = sm.t[1], frequency = theta3)
-    
-    # sm: sm.regression with optimal smoothing parameter
-    h.optimal5 = h.select(sm.t, kt.reference)
-    sm0        = sm.regression(sm.t, kt.reference, h = h.optimal5, eval.points = t0, model = "none", poly.index = 1, display = "none")
-    mu0        = theta1 * sm0$estimate
-    mu0        = ts(mu0, start = t0[1], frequency = 1)
-    
-    return(list(result, mu, mu0, tmin, tmax))
-}
-
-```
diff --git a/MuPoMo_referencecurve/README.md b/MuPoMo_referencecurve/README.md
deleted file mode 100644
index f967c98..0000000
--- a/MuPoMo_referencecurve/README.md
+++ /dev/null
@@ -1,51 +0,0 @@
-
-[<img src="https://github.com/QuantLet/Styleguide-and-FAQ/blob/master/pictures/banner.png" width="880" alt="Visit QuantNet">](http://quantlet.de/index.php?p=info)
-
-## [<img src="https://github.com/QuantLet/Styleguide-and-Validation-procedure/blob/master/pictures/qloqo.png" alt="Visit QuantNet">](http://quantlet.de/) **MuPoMo_referencecurve** [<img src="https://github.com/QuantLet/Styleguide-and-Validation-procedure/blob/master/pictures/QN2.png" width="60" alt="Visit QuantNet 2.0">](http://quantlet.de/d3/ia)
-
-```yaml
-
-Name of QuantLet : MuPoMo_referencecurve
-
-Published in : MuPoMo
-
-Description : 'Regenerates reference curve (common trend) based on normalized optimal theta
-parameters and smoothed original kt, and will be called in MuPoMo_main_multipop.'
-
-Keywords : time series, demography, mortality, population, normalization
-
-See also : 'MuPoMo_data, MuPoMo_optimization, MuPoMo_normalization, MuPoMo_main_twopop,
-MuPoMo_main_multipop, MuPoMo_bootstrap'
-
-Author : Lei Fang
-
-Submitted : Mon, June 13 2016 by Lei Fang
-
-```
-
-
-### R Code:
-```r
-referencecurve  = function(theta2, theta3, kt, kt.null) {
-    t           = time(kt)
-    sm.t        = theta3 * t + theta2  # time adjustment
-    t.reference = Sweden$year
-    ## common grid for kt and shifted kt.reference
-    tmin = max(min(t.reference), min(sm.t))
-    tmax = min(max(t.reference), max(sm.t))
-    i0   = which(t.reference >= tmin & t.reference <= tmax)
-    if (length(i0) > 0) {
-        t0  = t.reference[i0]
-        d   = data.frame(kt, sm.t)
-        # sm: sm.regression with optimal smoothing parameter
-        h.optimal6 = h.select(sm.t, kt)
-        sm  = sm.regression(sm.t, kt, h = h.optimal6, eval.points = t0, model = "none", poly.index = 1, display = "none")
-        mu1 = sm$estimate
-        mu  = ts(mu1, start = t0[1], frequency = 1)
-    } else {
-        mu  = kt.null
-    }
-    return(mu)
-}
-
-```

From fc3d7bf5ab6f3cdfb489ea87fb9a972388c4397a Mon Sep 17 00:00:00 2001
From: Lukas Borke <admin@quantnet.technology>
Date: Fri, 9 Dec 2016 15:03:24 +0100
Subject: [PATCH 29/63] auto create md

---
 MuPoMo_bootstrap/README.md | 240 +++++++++++++++++++++++++++++++++++++
 1 file changed, 240 insertions(+)
 create mode 100644 MuPoMo_bootstrap/README.md

diff --git a/MuPoMo_bootstrap/README.md b/MuPoMo_bootstrap/README.md
new file mode 100644
index 0000000..92f8a4c
--- /dev/null
+++ b/MuPoMo_bootstrap/README.md
@@ -0,0 +1,240 @@
+
+[<img src="https://github.com/QuantLet/Styleguide-and-FAQ/blob/master/pictures/banner.png" width="888" alt="Visit QuantNet">](http://quantlet.de/)
+
+## [<img src="https://github.com/QuantLet/Styleguide-and-FAQ/blob/master/pictures/qloqo.png" alt="Visit QuantNet">](http://quantlet.de/) **MuPoMo_bootstrap** [<img src="https://github.com/QuantLet/Styleguide-and-FAQ/blob/master/pictures/QN2.png" width="60" alt="Visit QuantNet 2.0">](http://quantlet.de/)
+
+```yaml
+
+Name of QuantLet : MuPoMo_bootstrap
+
+Published in : MuPoMo
+
+Description : 'Forecasts mortality rates based on a semi-parametric approach, and bootstraps time
+series with innovation to compute the prediction intervals. Uses random two countries to
+demonstrate.'
+
+Keywords : 'time series, demography, mortality, population, nonparametric smoothing, parametric
+modelling, Lee-Carter method, bootstrap'
+
+See also : 'MuPoMo_data, MuPoMo_optimization, MuPoMo_normalization, MuPoMo_referencecurve,
+MuPoMo_main_twopop, MuPoMo_main_multipop'
+
+Author : Lei Fang
+
+Submitted : Mon, June 13 2016 by Lei Fang
+
+Example : Prediction intervals at different levels, Histogram of theta1
+
+```
+
+![Picture1](Histogram of theta1.png)
+
+![Picture2](Prediction intervals at different levels.png)
+
+
+### R Code:
+```r
+# clear history and close windows
+rm(list=ls(all=TRUE))
+graphics.off()
+
+# please set working directory
+# setwd("C:/...")     # windows
+# setwd("/Users/...") # mac os
+# setwd("~/...")      # linux
+
+# install packages
+library(demography)
+library(rgl)
+library(sm)
+library(boot)
+library(tseries)
+
+# setting
+par(mar = c(5, 5, 2, 2), cex.axis = 1.5, cex.lab = 2)
+options(digits = 4)
+
+# load saved RData to reduce code-running time from previous procedure (MuPoMo_main_multipop.R)
+# load("~/.../MuPoMo_main_multipop.RData")
+
+# Bootstrap to resample from China's mortality time series to construct the CI for shape deviation parameters theta
+
+# Reference time series curve (unchanged). We use for comparing with resampled Japan's mortality TS
+kt.referencet = reference4
+# Original Japan's mortality TS, from which we are going to take TS bootstrap
+boot.data     = kt.Japan.female
+# Initialize theta values for optimazation
+theta         = theta4[16, ]
+
+### loss function
+loss = function(theta, t, kt, t.reference, kt.reference) {
+    ## assume theta[1]>0, theta[3]>0, if not, take absolute values
+    theta1 = abs(theta[1])
+    theta2 = theta[2]
+    theta3 = abs(theta[3])
+    
+    if (theta[1] < 0 | theta[3] < 0) 
+        warning("theta1 or theta3 <0, abs value is used")
+    # time adjustment
+    sm.t = (t.reference - theta2)/theta3  
+    ## common domain for kt and time-adjusted kt.reference
+    tmin = max(min(t), min(sm.t))
+    tmax = min(max(t), max(sm.t))
+    # index for common domain
+    i0 = which(t >= tmin & t <= tmax)
+    
+    if (length(i0) > 0) {
+        t0 = t[i0]
+        ## smooth interpolation of shifted kt.reference on common grid
+        dref = data.frame(sm.t = sm.t, kt.reference = kt.reference)
+        
+        # sm: sm.regression with optimal smoothing parameter 
+        h.optimal3 = h.select(sm.t, kt.reference) 
+        sm = sm.regression(sm.t, kt.reference, h = h.optimal3, eval.points = t0, model = 'none', poly.index = 1, display = 'none') 
+        mu = theta1 * sm$estimate
+
+        ## mean squared error at common grid points
+        mse = mean((kt[i0] - mu)^2)  # mse of kt and the modelled one
+    } else {
+        mse = 1e+09
+    }
+    return(mse)
+}
+
+# Construct the 'statistic' function which is needed and very important in 'tsboot' tsboot (tseries, statistic, R, l = NULL, sim =
+# 'model',...)
+boot.func = function(kt) {
+    t = time(kt)
+    t.reference = time(kt.reference)
+    ### parameter estimation
+    conv   = 1
+    theta0 = theta
+    while (conv != 0) {
+        # check convergence
+        out    = optim(theta0, loss, gr = NULL, t, kt, t.reference, kt.reference, control = list(maxit = 1000))  # optimization
+        conv   = out$convergence
+        theta0 = out$par
+    }
+    # add constraint on theta2
+    if (out$par[2] >= -200 & out$par[2] <= 200) 
+        temp.par = out$par else temp.par = theta
+    result = c(temp.par, out$value, out$convergence)
+}
+
+# simulate time series with innovation
+bootdata.fit = auto.arima(boot.data)
+sim = 500
+plot(boot.data, xlab = "Time", ylab = "Kt", ylim = c(-150, 70), col = "blue", lwd = 10)
+
+for (i in 1:sim) {
+    nam5  = paste("sim.ts", i, sep = ".")
+    # simulate time seriese based on bootstrap of innovation/error term in ARIMA fitting model
+    temp5 = simulate(bootdata.fit, nsim = length(boot.data), future = FALSE, bootstrap = TRUE)
+    assign(nam5, temp5)
+    # time series test on plot
+    lines(temp5, col = "grey")
+}
+
+# compute parameters theta's based on bootstrapped time series
+theta.boot = matrix(rep(c(0, 0, 0, 0, 0), sim), sim, 5, byrow = TRUE)
+
+for (i in 1:sim) {
+    theta.boot[i, ] = boot.func(eval(parse(text = paste("sim.ts", i, sep = "."))))
+}
+
+# plot test
+hist(theta.boot[, 1], xlab = "theta 1", main = "Histogram of theta 1")
+quantile(theta.boot[, 1])
+
+hist(theta.boot[, 2][which(theta.boot[, 2] >= -100 & theta.boot[, 2] <= 100)], xlab = "theta 2", 
+     main = "Histogram of theta 2", xlim = c(-5, 5), breaks = 10)
+quantile(theta.boot[, 2])
+
+hist(theta.boot[, 3][which(theta.boot[, 3] >= 0.8 & theta.boot[, 3] <= 1.2)], xlab = "theta 3", 
+     main = "Histogram of theta 3", xlim = c(0.93, 0.99), breaks = 10)
+quantile(theta.boot[, 3])
+
+# forecast with estimated parameters from bootstrap
+boot.forecast = function(theta, kt, kt.reference) {
+    t = time(kt)
+    t.reference = time(kt.reference)
+    ### check results on graph
+    theta1 = abs(theta[1])
+    theta2 = theta[2]
+    theta3 = abs(theta[3])
+    # time adjustment
+    sm.t = (t.reference - theta2)/theta3
+    ## common grid for kt and shifted kt.reference
+    tmin = max(min(t), min(sm.t))
+    tmax = min(max(t), max(sm.t))
+    i0   = which(t >= tmin & t <= tmax)
+    t0   = t[i0]
+    ## shifted curves (kt.hat)
+    dref = data.frame(sm.t = sm.t, kt.reference = kt.reference)
+    # sm: sm.regression with optimal smoothing parameter
+    h.optimal4 = h.select(sm.t, kt.reference)
+    sm = sm.regression(sm.t, kt.reference, h = h.optimal4, eval.points = sm.t, model = "none", poly.index = 1, display = "none")
+    mu = theta1 * sm$estimate
+
+    mu = ts(mu, start = sm.t[1], frequency = theta3)
+    
+    # sm: sm.regression with optimal smoothing parameter
+    h.optimal5 = h.select(sm.t, kt.reference)
+    sm0 = sm.regression(sm.t, kt.reference, h = h.optimal5, eval.points = t0, model = "none", poly.index = 1, display = "none")
+    mu0 = theta1 * sm0$estimate
+
+    mu0 = ts(mu0, start = t0[1], frequency = 1)
+    
+    return(list(mu, mu0, tmin, tmax))
+}
+
+# forecast
+plot(forecast(bootdata.fit, h = 40, level = 95), xlab = "Time", ylab = "Kt", xlim = c(1828, 2050), ylim = c(-200, 150))
+lines(kt.referencet, col = "blue", lwd = 5)
+lines(boot.data, col = "red", lwd = 5)
+
+for (i in 1:sim) {
+    temp  = boot.forecast(theta.boot[i, 1:3], boot.data, kt.reference)
+    nam12 = paste("shift.kt.boot", i, sep = ".")
+    assign(nam12, temp[[2]])
+    nam15 = paste("mu.boot", i, sep = ".")
+    assign(nam15, temp[[1]])
+    lines(temp[[2]], col = "green")  
+    lines(temp[[1]], col = "grey")  
+}
+
+# prediction interval
+for (i in 2010:2050) {
+    nam = matrix(0, 1, 500)
+    for (j in 1:sim) {
+        if (max(time(eval(parse(text = paste("mu.boot", j, sep = "."))))) >= i) 
+            nam[j] = window(eval(parse(text = paste("mu.boot", j, sep = "."))), i)[1] else nam[j] = NA
+    }
+    nam1 = paste("ts", i, sep = ".")
+    assign(nam1, nam)
+    nam2 = paste("ts", i, 5, sep = ".")
+    assign(nam2, quantile(nam, probs = seq(0, 1, 0.05), na.rm = T)[2])
+    nam3 = paste("ts", i, 95, sep = ".")
+    assign(nam3, quantile(nam, probs = seq(0, 1, 0.05), na.rm = T)[20])
+    nam4 = paste("ts", i, 20, sep = ".")
+    assign(nam4, quantile(nam, probs = seq(0, 1, 0.05), na.rm = T)[5])
+    nam5 = paste("ts", i, 80, sep = ".")
+    assign(nam5, quantile(nam, probs = seq(0, 1, 0.05), na.rm = T)[17])
+}
+
+for (j in c(5, 20, 80, 95)) {
+    ts.temp = ts(0, start = 2010, end = 2040, frequency = 1)
+    for (i in 2010:2040) {
+        ts.temp[i - 2009] = eval(parse(text = paste("ts", i, j, sep = ".")))
+    }
+    nam6 = paste("ts.forecast", j, sep = ".")
+    assign(nam6, ts.temp)
+}
+
+# plot
+plot(boot.data, lwd = 5, xlab = "Time", ylab = "Kt", xlim = c(1828, 2050), ylim = c(-200, 150))
+polygon(c(2010:2040, rev(2010:2040)), c(ts.forecast.5, rev(ts.forecast.95)), col = "yellow", border = FALSE)
+polygon(c(2010:2040, rev(2010:2040)), c(ts.forecast.20, rev(ts.forecast.80)), col = "Gray", border = FALSE)
+lines(kt.referencet, col = "blue", lwd = 5)
+lines(mu.China.4, col = 5, lty = 2, lwd = 4)
+```

From 5c989ecca8fa10991ad3271fe79c7dd415015ad9 Mon Sep 17 00:00:00 2001
From: Lukas Borke <admin@quantnet.technology>
Date: Fri, 9 Dec 2016 15:03:26 +0100
Subject: [PATCH 30/63] auto create md

---
 MuPoMo_data/README.md | 59 +++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 59 insertions(+)
 create mode 100644 MuPoMo_data/README.md

diff --git a/MuPoMo_data/README.md b/MuPoMo_data/README.md
new file mode 100644
index 0000000..6c88804
--- /dev/null
+++ b/MuPoMo_data/README.md
@@ -0,0 +1,59 @@
+
+[<img src="https://github.com/QuantLet/Styleguide-and-FAQ/blob/master/pictures/banner.png" width="888" alt="Visit QuantNet">](http://quantlet.de/)
+
+## [<img src="https://github.com/QuantLet/Styleguide-and-FAQ/blob/master/pictures/qloqo.png" alt="Visit QuantNet">](http://quantlet.de/) **MuPoMo_data** [<img src="https://github.com/QuantLet/Styleguide-and-FAQ/blob/master/pictures/QN2.png" width="60" alt="Visit QuantNet 2.0">](http://quantlet.de/)
+
+```yaml
+
+Name of QuantLet : MuPoMo_data
+
+Published in : MuPoMo
+
+Description : 'Reads data from Human Mortality Database and calculate kt, and will be called in
+MuPoMo_main_twopop and MuPoMo_main_multipop.'
+
+Keywords : 'time series, demography, mortality, Lee-Carter method, population, Human Mortality
+Database'
+
+See also : 'MuPoMo_optimization, MuPoMo_normalization, MuPoMo_referencecurve, MuPoMo_main_twopop,
+MuPoMo_main_multipop, MuPoMo_bootstrap'
+
+Author : Lei Fang
+
+Submitted : Mon, June 13 2016 by Lei Fang
+
+```
+
+
+### R Code:
+```r
+# read multi-pop female mortality rates from Human Mortality Database
+shortnames.all = c("AUS", "AUT", "BLR", "BGR", "CAN", "CHL", "CZE", "DNK", "EST", "FIN", "FRATNP", "DEUTNP", "HUN", "ISL", "IRL", 
+    "ISR", "ITA", "JPN", "LVA", "LTU", "LUX", "NLD", "NZL_NP", "NOR", "POL", "PRT", "RUS", "SVK", "SVN", "ESP", "CHE", "TWN", "GBR_NP", 
+    "USA", "SWE")
+names.all = c("Australia", "Austria", "Belarus", "Bulgaria", "Canada", "Chile", "CzechRepublic", "Denmark", "Estonia", "Finland", 
+    "France", "Germany", "Hungary", "Iceland", "Ireland", "Israel", "Italy", "Japan", "Latvia", "Lithuania", "Luxembourg", "Netherlands", 
+    "NewZealand", "Norway", "Poland", "Portugal", "Russia", "Slovakia", "Slovenia", "Spain", "Switzerland", "Taiwan", "UnitedKingdom", 
+    "USA", "Sweden")
+
+loop.all = length(names.all)
+for (i in 1:loop.all) {
+    nam1 = paste(names.all[i])
+    # read data from Human Mortality Database (HMD: http://www.mortality.org/)
+    # you need register on HMD to access a free account accound and set up your password
+    assign(nam1, hmd.mx(shortnames.all[i], "account", "password", names.all[i]))
+    temp1 = hmd.mx(shortnames.all[i], "account", "password", names.all[i])
+    nam2  = paste(names.all[i], "lca.female", sep = ".")
+    # Lee-Carter method
+    assign(nam2, lca(temp1, series = "female", adjust = "dt", interpolate = TRUE))
+    temp2 = lca(temp1, series = "female", adjust = "dt", interpolate = TRUE)
+    nam3  = paste("ax", names.all[i], "female", sep = ".")  # ax
+    assign(nam3, temp2$ax)
+    nam4  = paste("bx", names.all[i], "female", sep = ".")  # bx
+    assign(nam4, temp2$bx)
+    nam5  = paste("kt", names.all[i], "female", sep = ".")  # kt
+    assign(nam5, temp2$kt)
+}
+
+
+```

From c0d4caaa08bc1abc022a55eb13fbe203767fb56a Mon Sep 17 00:00:00 2001
From: Lukas Borke <admin@quantnet.technology>
Date: Fri, 9 Dec 2016 15:03:27 +0100
Subject: [PATCH 31/63] auto create md

---
 MuPoMo_main_multipop/README.md | 192 +++++++++++++++++++++++++++++++++
 1 file changed, 192 insertions(+)
 create mode 100644 MuPoMo_main_multipop/README.md

diff --git a/MuPoMo_main_multipop/README.md b/MuPoMo_main_multipop/README.md
new file mode 100644
index 0000000..5156cc8
--- /dev/null
+++ b/MuPoMo_main_multipop/README.md
@@ -0,0 +1,192 @@
+
+[<img src="https://github.com/QuantLet/Styleguide-and-FAQ/blob/master/pictures/banner.png" width="888" alt="Visit QuantNet">](http://quantlet.de/)
+
+## [<img src="https://github.com/QuantLet/Styleguide-and-FAQ/blob/master/pictures/qloqo.png" alt="Visit QuantNet">](http://quantlet.de/) **MuPoMo_main_multipop** [<img src="https://github.com/QuantLet/Styleguide-and-FAQ/blob/master/pictures/QN2.png" width="60" alt="Visit QuantNet 2.0">](http://quantlet.de/)
+
+```yaml
+
+Name of QuantLet : MuPoMo_main_multipop
+
+Published in : MuPoMo
+
+Description : 'Estimates and forecasts mortality rates based on a semi-parametric approach, which
+applies parametric modelling for multiple nonparametric smoothed curves with the shape-related
+nonlinear variation.'
+
+Keywords : 'time series, demography, mortality, population, nonparametric smoothing, parametric
+modelling, Lee-Carter method'
+
+See also : 'MuPoMo_data, MuPoMo_optimization, MuPoMo_normalization, MuPoMo_referencecurve,
+MuPoMo_main_twopop, MuPoMo_bootstrap'
+
+Author : Lei Fang
+
+Submitted : Mon, June 13 2016 by Lei Fang
+
+Example : Multi-Population model with German data, Multi-Population model with Japanese data
+
+```
+
+![Picture1](Multi-Population model with German data.png)
+
+![Picture2](Multi-Population model with Japanese data.png)
+
+
+### R Code:
+```r
+# clear history and close windows
+rm(list=ls(all=TRUE))
+graphics.off()
+
+# please set working directory
+# setwd("C:/...")     # windows
+# setwd("/Users/...") # mac os
+# setwd("~/...")      # linux
+
+# install packages
+library(demography)
+library(rgl)
+library(sm)
+
+# set plot
+par(mar = c(5, 5, 2, 2), cex.axis = 1.5, cex.lab = 2)
+
+# recall self-defined functions
+source('MuPoMo_data.R')
+source("MuPoMo_optimization.R")
+source("MuPoMo_normalization.R")
+source("MuPoMo_referencecurve.R")
+
+# set bandwidth
+bw.default = 2.5
+
+## descriptive plot plot kt of 35 countries
+plot(kt.Sweden.female, type = "l", ylim = c(-250, 150), xlab = "Time", ylab = "kt", main = "Original Kt (35 countries)")
+for (i in 1:(loop.all - 1)) {
+    lines(eval(parse(text  = paste("kt.", names.all[i], ".female", sep = ""))), col = i)
+}
+
+##### common trend
+#### initial setting nonparametric smoothing 35 countries
+for (i in 1:loop.all) {
+    kt = eval(parse(text = paste("kt.", names.all[i], ".female", sep = "")))
+    t  = eval(parse(text = paste(names.all[i])))$year
+    d  = data.frame(kt, t)
+    # sm: sm.regression with optimal smoothing parameter
+    h.optimal1 = h.select(t, kt)
+    sm         = sm.regression(t, kt, h = h.optimal1, eval.points = t, model = "none", poly.index = 1, display = "none")
+    nam6       = paste("sm.kt", names.all[i], "female", sep = ".")
+    temp6      = ts(sm$estimate, start = t[1], frequency = 1)
+    assign(nam6, temp6)
+}
+
+## plot smoothed kt of 35 countries
+plot(sm.kt.Sweden.female, type = "l", ylim = c(-250, 150), xlab = "Time", ylab = "kt", main = "Smoothed Kt (35 countries)")
+for (i in 1:(loop.all - 1)) {
+    lines(eval(parse(text = paste("sm.kt.", names.all[i], ".female", sep = ""))), col = i)
+}
+
+#### intial values of thetas 
+### remove Russia, Lithuavia, Latvia, Estonia and Belarus 
+### set up the initial reference curve based on 31 countries
+names.31 = c("Australia", "Austria", "Bulgaria", "Canada", "Chile", "CzechRepublic", "Denmark", "Finland", "France", "Germany", "Hungary", 
+    "Iceland", "Ireland", "Israel", "Italy", "Japan", "Luxembourg", "Netherlands", "NewZealand", "Norway", "Poland", "Portugal", "Slovakia", 
+    "Slovenia", "Spain", "Switzerland", "Taiwan", "UnitedKingdom", "USA", "Sweden")
+loop.31  = length(names.31)
+merge1   = sm.kt.Australia.female
+for (i in 1:(loop.31 - 1)) {
+    nam7  = paste("merge", i + 1, sep = "")
+    temp3 = merge.zoo(eval(parse(text = paste("merge", i, sep = ""))), eval(parse(text = paste("sm.kt.", names.31[i + 1], ".female", 
+        sep = ""))))
+    assign(nam7, temp3)
+}
+reference0.temp = rowMeans(merge31, na.rm = TRUE)
+reference0      = ts(reference0.temp, start = Sweden$year[1], frequency = 1)
+
+## plot the reference curve among all 31 smoothed curves
+plot(sm.kt.Sweden.female, type = "l", ylim = c(-250, 150), xlab = "Time", ylab = "kt", main = "Reference Curve vs. Smoothed Kt (31 countries)")
+for (i in 1:loop.31) {
+    lines(eval(parse(text = paste("sm.kt.", names.31[i], ".female", sep = ""))), col = i)
+}
+lines(reference0, lwd = 4, col = "red")
+
+##### begin loop
+theta0    = matrix(rep(c(1, 0, 1), loop.31), loop.31, 3, byrow = TRUE)
+iteration = 5
+for (j in 1:iteration) {
+    ### find the optimal initial theta based on the reference curve
+    theta        = eval(parse(text = paste("theta", j - 1, sep = "")))
+    kt.reference = eval(parse(text = paste("reference", j - 1, sep = "")))
+    results      = matrix(NA, loop.31, 5)  # c(theta1,theta2,theta3, loss, convergence)
+    for (i in 1:loop.31) {
+        kt           = eval(parse(text = paste("sm.kt.", names.31[i], ".female", sep = "")))
+        tt           = time(kt)
+        ltt          = length(tt)
+        temp4        = optimization(theta[i, ], kt, kt.reference)
+        results[i, ] = temp4[[1]]
+        nam12        = paste("shift.kt", names.31[i], j, sep = ".")
+        assign(nam12, temp4[[3]])
+        nam15        = paste("mu", names.31[i], j, sep = ".")
+        assign(nam15, temp4[[2]])
+        pdf(paste("plot_", j, "_", i, ".pdf", sep = ""))
+        par(mar = c(5, 5, 2, 2))
+        plot(eval(parse(text = paste("kt.", names.31[i], ".female", sep = ""))), ylim = c(-250, 150), xlim = c(1750, 2020), type = "p", 
+            xlab = "Time", ylab = "kt", main = paste(names.31[i], tt[1], "--", tt[ltt], ":step", j))
+        lines(kt, col = 2)  # sm.kt
+        lines(kt.reference, col = 4, lwd = 2)  # reference
+        lines(temp4[[2]], col = 5, lty = 5)  # new kt
+        lines(temp4[[3]], col = 5, lwd = 2)  # new kt
+        abline(v = temp4[[4]], col = "gray", lty = 5)
+        abline(v = temp4[[5]], col = "gray", lty = 5)
+        # legend('topright', legend=c('kt', 'sm.kt', 'k0', 'kt.hat'), col=c(1,2,4,5), lty=1)
+        dev.off()
+    }
+    nam16 = paste("results", j, sep = "")
+    assign(nam16, results)
+    nam18 = paste("theta", j, sep = "")
+    assign(nam18, results[, 1:3])
+    
+    ## plot shifted kt of 31 countries and the reference curve of previous step
+    plot(kt.reference, type = "l", ylim = c(-250, 150), xlab = "Time", ylab = "kt", lwd = 4, col = "red", main = paste("Reference Curve vs. Shifted Kt (31 countries): step", 
+        j - 1))
+    for (i in 1:loop.31) {
+        lines(eval(parse(text = paste("shift.kt", names.31[i], j, sep = "."))), col = i)
+    }
+    
+    # construct optimal.theta.matrix and normalize optimal theta
+    optimal.theta.matrix          = results[, 1:3]
+    standard.optimal.theta.matrix = normalization(optimal.theta.matrix)
+    
+    # construct new reference curve
+    for (i in 1:loop.31) {
+        nam13 = paste("shift.kt", names.31[i], "standard", sep = ".")
+        assign(nam13, referencecurve(standard.optimal.theta.matrix[i, 2], standard.optimal.theta.matrix[i, 3], eval(parse(text = paste("sm.kt.", 
+            names.31[i], ".female", sep = ""))), eval(parse(text = paste("shift.kt", names.31[i], j, sep = ".")))))
+    }
+    merge1.1  = shift.kt.Australia.standard
+    for (i in 1:(loop.31 - 1)) {
+        nam7  = paste("merge1", i + 1, sep = ".")
+        temp3 = merge.zoo(eval(parse(text = paste("merge1", i, sep = "."))), eval(parse(text = paste("shift.kt", names.31[i + 1], 
+            "standard", sep = "."))))
+        assign(nam7, temp3)
+    }
+    reference.temp           = rowMeans(merge1.31, na.rm = TRUE)
+    reference.temp.nonsmooth = ts(reference.temp, start = min(index(merge1.31)), frequency = 1)
+    t.temp                   = time(reference.temp.nonsmooth)
+    
+    ## smooth the updated reference curve
+    # sm: sm.regression
+    temp17 = sm.regression(t.temp, reference.temp.nonsmooth, eval.points = t.temp, model = "none", poly.index = 1, display = "none")
+    nam17  = paste("reference", j, sep = "")
+    assign(nam17, ts(temp17$estimate, start = t.temp[1], frequency = 1))
+    
+    ## plot the updated reference curve among all 31 shifted curves
+    plot(eval(parse(text = paste("reference", j, sep = ""))), lwd = 4, col = "red", type = "l", ylim = c(-250, 150), xlab = "Time", 
+        ylab = "kt", main = paste("Updated Reference Curve vs. Shifted Kt (31 countries): step", j))
+    for (i in 1:loop.31) {
+        lines(eval(parse(text = paste("shift.kt", names.31[i], j, sep = "."))), col = i)
+        lines(eval(parse(text = paste("sm.kt.", names.31[i], ".female", sep = ""))), col = "grey")
+    }
+    lines(eval(parse(text = paste("reference", j - 1, sep = ""))), col = "blue", lwd = 3, lty = 5)
+}
+```

From 68d187ed4d8f32410243f420258bd0e8b1710f3a Mon Sep 17 00:00:00 2001
From: Lukas Borke <admin@quantnet.technology>
Date: Fri, 9 Dec 2016 15:03:29 +0100
Subject: [PATCH 32/63] auto create md

---
 MuPoMo_main_twopop/README.md | 195 +++++++++++++++++++++++++++++++++++
 1 file changed, 195 insertions(+)
 create mode 100644 MuPoMo_main_twopop/README.md

diff --git a/MuPoMo_main_twopop/README.md b/MuPoMo_main_twopop/README.md
new file mode 100644
index 0000000..44c5dd7
--- /dev/null
+++ b/MuPoMo_main_twopop/README.md
@@ -0,0 +1,195 @@
+
+[<img src="https://github.com/QuantLet/Styleguide-and-FAQ/blob/master/pictures/banner.png" width="888" alt="Visit QuantNet">](http://quantlet.de/)
+
+## [<img src="https://github.com/QuantLet/Styleguide-and-FAQ/blob/master/pictures/qloqo.png" alt="Visit QuantNet">](http://quantlet.de/) **MuPoMo_main_twopop** [<img src="https://github.com/QuantLet/Styleguide-and-FAQ/blob/master/pictures/QN2.png" width="60" alt="Visit QuantNet 2.0">](http://quantlet.de/)
+
+```yaml
+
+Name of QuantLet : MuPoMo_main_twopop
+
+Published in : MuPoMo
+
+Description : 'Estimates and forecasts mortality rates based on a semi-parametric approach, which
+applies parametric modelling for multiple nonparametric curves with the shape-related nonlinear
+variation. Uses random two countries to demonstrate two-country case.'
+
+Keywords : 'time series, demography, mortality, population, nonparametric smoothing, parametric
+modelling, Lee-Carter method, contour'
+
+See also : 'MuPoMo_data, MuPoMo_optimization, MuPoMo_normalization, MuPoMo_referencecurve,
+MuPoMo_main_multipop, MuPoMo_bootstrap'
+
+Author : Lei Fang
+
+Submitted : Mon, June 13 2016 by Lei Fang
+
+Example : 'Time shift at different levels, Loss function of theta2, Loss surface 3D, Contour plot
+of theta2 and theta4, Model fit and forecast'
+
+```
+
+![Picture1](Contour plot of theta2 and theta4.png)
+
+![Picture2](Loss function of theta2.png)
+
+![Picture3](Loss surface 3D.png)
+
+![Picture4](Model fit and forecast.png)
+
+![Picture5](Time shift at different levels.png)
+
+
+### R Code:
+```r
+# clear history and close windows
+rm(list=ls(all=TRUE))
+graphics.off()
+
+# please set working directory
+# setwd("C:/...")     # windows
+# setwd("/Users/...") # mac os
+# setwd("~/...")      # linux
+
+# install packages
+library(demography)
+library(rgl)
+library(sm)
+
+# set plot
+par(mar = c(5, 5, 2, 2), cex.axis = 1.5, cex.lab = 2)
+
+# recall self-defined functions
+# read data and compute kt based on Lee-Carter Model via source('data.R')
+source('MuPoMo_data.R')
+source("MuPoMo_optimization.R")
+
+# choose two countries' kt for this analysis
+kt1 = kt.China.female
+kt2 = kt.Japan.female
+
+# set bandwidth for smoothing curves
+bw.default     = 2.5
+
+# plot kt
+plot(kt2, type = "l", col = "blue", lwd = 4, xlab = "Time", ylab = "Kt")
+lines(kt1, col = "red", lwd = 4)
+
+# shift movement of the two smoothed countries
+t1         = 1994:2010 # differ based on the chosen country
+d1         = data.frame(time(kt1), kt1)
+h.optimal1 = h.select(time(kt1), kt1)
+sm1        = sm.regression(time(kt1), kt1, h = h.optimal1, eval.points = time(kt1), model = "none", poly.index = 1, display = "none")
+sm.kt1     = sm1$estimate  # smoothed kt1
+
+t2         = 1947:2012 # differ based on the chosen country
+d2         = data.frame(time(kt2), kt2)
+h.optimal2 = h.select(time(kt2), kt2)
+sm2        = sm.regression(time(kt2), kt2, h = h.optimal2, eval.points = time(kt2), model = "none", poly.index = 1, display = "none")
+sm.kt2     = sm2$estimate  # smoothed kt2
+
+plot(t2, sm.kt2, type = "l", col = "blue", lwd = 4, xlab = "Time", ylab = "Kt")
+lines(kt2, col = "red", lwd = 4)
+lines(t1, sm.kt1, lwd = 4)
+lines(kt1, col = "darkgreen", lwd = 4)
+lines(t2 + 20, sm.kt2, lwd = 4, lty = 2) # differ based on the chosen country
+lines(t2 + 25, sm.kt2, lwd = 4, lty = 3)
+lines(t2 + 30, sm.kt2, lwd = 4, lty = 4)
+
+# time delay
+plot(t2, sm.kt2, type = "l", col = "blue", lwd = 4, xlab = "Time", ylab = "Kt")
+lines(t1, sm.kt1, lwd = 4)
+lines(t2 + 23, sm.kt2, lwd = 4, lty = 4, col = "blue") # differ based on the chosen country
+
+# vertical shift
+plot(t2, sm.kt2, type = "l", col = "blue", lwd = 4, xlab = "Time", ylab = "Kt")
+lines(t1, sm.kt1, lwd = 4)
+lines(t2, sm.kt2 + 85, lwd = 4, lty = 4, col = "blue") # differ based on the chosen country
+
+# optimization
+theta.2pop  = c(1, -23, 1) # differ based on the chosen country
+result.2pop = optimization(theta.2pop, kt1, kt2)
+
+# plot optimized movement
+plot(t2, sm.kt2, type = "l", col = 4, lwd = 4, xlab = "Time", ylab = "Kt")
+lines(kt2, type = "p", lwd = 3)
+lines(t1, sm.kt1, lwd = 4, col = 2)
+lines(kt1, type = "p", lwd = 3)
+lines(result.2pop[[2]], col = 5, lty = 5)  #
+lines(result.2pop[[3]], col = 5, lwd = 3)  #
+abline(v = result.2pop[[4]], col = "gray", lty = 5)
+abline(v = result.2pop[[5]], col = "gray", lty = 5)
+
+# plot loss function
+loss = function(theta1, theta2, theta3, theta4, t, kt, t.reference, kt.reference) {
+    sm.t = (t.reference - theta2)/theta3  # time adjustment
+    ## common domain for kt and time-adjusted kt.reference
+    tmin = max(min(t), min(sm.t))
+    tmax = min(max(t), max(sm.t))
+    i0 = which(t >= tmin & t <= tmax)  # index for common domain
+    if (length(i0) > 0) {
+        t0 = t[i0]
+        ## smooth interpolation of shifted kt.reference on common grid
+        dref = data.frame(sm.t = sm.t, kt.reference = kt.reference)
+        # sm: sm.regression with optimal smoothing parameter
+        h.optimal3 = h.select(sm.t, kt.reference)
+        sm = sm.regression(sm.t, kt.reference, h = h.optimal3, eval.points = t0, model = "none", poly.index = 1, display = "none")
+        mu = theta1 * sm$estimate + theta4
+        ## mean squared error at common grid points
+        mse = mean((kt[i0] - mu)^2)  # mse of kt and the modelled one
+    } else {
+        mse = 1e+09
+    }
+    return(mse)
+}
+
+# plot loss function of theta2 and theta4
+vtheta2 = seq(-30, 10, len = 100) # differ based on the chosen country
+vtheta4 = seq(0, 100, len = 100) # differ based on the chosen country
+npar    = length(vtheta2)
+res     = matrix(rep(0, 10000), 100, 100)
+for (i in 1:npar) {
+    for (l in 1:npar) {
+        res[i, l] = loss(1, vtheta2[i], 1, vtheta4[l], t1, kt1, t2, kt2)
+    }
+    res[i, l] = loss(1, vtheta2[i], 1, vtheta4[l], t1, kt1, t2, kt2)
+}
+
+persp3d(vtheta2, vtheta4, res, col = "blue", xlab = "theta2", ylab = "theta4", zlab = "Loss")
+
+resnew = res * (res < 5000)
+persp3d(vtheta2, vtheta4, resnew, col = "blue", xlab = "theta2", ylab = "theta4", zlab = "Loss")
+
+# contour plot
+contour(vtheta2, vtheta4, resnew, col = rainbow(20), nlevels = 20, lwd = 1, xlim = c(-23, 0), ylim = c(0, 80))
+contour(vtheta2, vtheta4, res, col = rainbow(20), nlevels = 70, lwd = 1, xlim = c(-23, 0), ylim = c(0, 80), zlim = c(0, 100))
+contour(vtheta2, vtheta4, res, col = rainbow(20), nlevels = 70, lwd = 1, xlim = c(-10, -2), ylim = c(40, 80), zlim = c(0, 100))
+
+# plot loss function of theta2
+vtheta22 = seq(-50, 0, len = 100) # differ based on the chosen country
+npar2    = length(vtheta22)
+res2     = rep(0, 100)
+for (i in 1:npar2) {
+    res2[i] = loss(1, vtheta22[i], 1, 0, t1, kt1, t2, kt2)
+}
+plot(vtheta22, res2, col = "blue", xlab = "theta2", ylab = "Loss", type = "l", lwd = 4)
+
+# plot loss function of theta4
+vtheta42 = seq(40, 140, len = 100) # differ based on the chosen country
+npar3    = length(vtheta42)
+res3     = rep(0, 100)
+for (i in 1:npar3) {
+    res3[i] = loss(1, 0, 1, vtheta42[i], t1, kt1, t2, kt2)
+}
+plot(vtheta42, res3, col = "blue", xlab = "theta4", ylab = "Loss", type = "l", lwd = 4)
+
+# forecast
+plot(t2, sm.kt2, type = "l", col = 4, lwd = 4, xlab = "Time", ylab = "Kt", xlim = c(1947, 2035))
+lines(kt2, type = "p", lwd = 3)
+lines(t1, sm.kt1, lwd = 4, col = 2)
+lines(kt1, type = "p", lwd = 3)
+lines(result.2pop[[2]], col = 4, lty = 5, lwd = 3)  #
+lines(result.2pop[[3]], col = "purple", lwd = 3)  #
+abline(v = result.2pop[[4]], col = "gray", lty = 5)
+abline(v = result.2pop[[5]], col = "gray", lty = 5)
+
+```

From b5aa1c9747684d47d1c14e1427f291f01c4f8b1a Mon Sep 17 00:00:00 2001
From: Lukas Borke <admin@quantnet.technology>
Date: Fri, 9 Dec 2016 15:03:30 +0100
Subject: [PATCH 33/63] auto create md

---
 MuPoMo_normalization/README.md | 50 ++++++++++++++++++++++++++++++++++
 1 file changed, 50 insertions(+)
 create mode 100644 MuPoMo_normalization/README.md

diff --git a/MuPoMo_normalization/README.md b/MuPoMo_normalization/README.md
new file mode 100644
index 0000000..a68dbef
--- /dev/null
+++ b/MuPoMo_normalization/README.md
@@ -0,0 +1,50 @@
+
+[<img src="https://github.com/QuantLet/Styleguide-and-FAQ/blob/master/pictures/banner.png" width="888" alt="Visit QuantNet">](http://quantlet.de/)
+
+## [<img src="https://github.com/QuantLet/Styleguide-and-FAQ/blob/master/pictures/qloqo.png" alt="Visit QuantNet">](http://quantlet.de/) **MuPoMo_normalization** [<img src="https://github.com/QuantLet/Styleguide-and-FAQ/blob/master/pictures/QN2.png" width="60" alt="Visit QuantNet 2.0">](http://quantlet.de/)
+
+```yaml
+
+Name of QuantLet : MuPoMo_normalization
+
+Published in : MuPoMo
+
+Description : 'Normalizes optimal shape variation parameters theta estimated from
+MuPoMo_optimization, and will be called in MuPoMo_main_multipop.'
+
+Keywords : time series, demography, mortality, population, normalization
+
+See also : 'MuPoMo_data, MuPoMo_optimization, MuPoMo_referencecurve, MuPoMo_main_twopop,
+MuPoMo_main_multipop, MuPoMo_bootstrap'
+
+Author : Lei Fang
+
+Submitted : Mon, June 13 2016 by Lei Fang
+
+```
+
+
+### R Code:
+```r
+normalization  = function(theta) {
+    theta.temp = colSums(theta)
+    for (i in 1:loop.31) {
+        nam10  = paste("normal.theta", names.31[i], 1, sep = ".")
+        assign(nam10, loop.31 * theta[i, 1]/theta.temp[1])
+        nam11  = paste("normal.theta", names.31[i], 3, sep = ".")
+        assign(nam11, loop.31 * theta[i, 3]/theta.temp[3])
+        nam12  = paste("normal.theta", names.31[i], 2, sep = ".")
+        assign(nam12, theta[i, 2] - theta.temp[2]/loop.31)
+        nam14  = paste("normal.theta", names.31[i], sep = ".")
+        assign(nam14, c(eval(parse(text = paste("normal.theta", names.31[i], 1, sep = "."))), eval(parse(text = paste("normal.theta", 
+            names.31[i], 2, sep = "."))), eval(parse(text = paste("normal.theta", names.31[i], 3, sep = ".")))))
+    }
+    ll = list()
+    for (i in 1:loop.31) {
+        ll[[i]]  = c(eval(parse(text = paste("normal.theta", names.31[i], sep = "."))))
+    }
+    normal.theta = do.call(rbind, ll)
+    return(normal.theta)
+}
+
+```

From 00b381473d82c2d6404ce702320eef733c8ae7f8 Mon Sep 17 00:00:00 2001
From: Lukas Borke <admin@quantnet.technology>
Date: Fri, 9 Dec 2016 15:03:31 +0100
Subject: [PATCH 34/63] auto create md

---
 MuPoMo_optimization/README.md | 108 ++++++++++++++++++++++++++++++++++
 1 file changed, 108 insertions(+)
 create mode 100644 MuPoMo_optimization/README.md

diff --git a/MuPoMo_optimization/README.md b/MuPoMo_optimization/README.md
new file mode 100644
index 0000000..bca74c7
--- /dev/null
+++ b/MuPoMo_optimization/README.md
@@ -0,0 +1,108 @@
+
+[<img src="https://github.com/QuantLet/Styleguide-and-FAQ/blob/master/pictures/banner.png" width="888" alt="Visit QuantNet">](http://quantlet.de/)
+
+## [<img src="https://github.com/QuantLet/Styleguide-and-FAQ/blob/master/pictures/qloqo.png" alt="Visit QuantNet">](http://quantlet.de/) **MuPoMo_optimization** [<img src="https://github.com/QuantLet/Styleguide-and-FAQ/blob/master/pictures/QN2.png" width="60" alt="Visit QuantNet 2.0">](http://quantlet.de/)
+
+```yaml
+
+Name of QuantLet : MuPoMo_optimization
+
+Published in : MuPoMo
+
+Description : 'Optimizes shape variation parameters theta based on kt and reference curve to update
+new kt, and will be called in MuPoMo_main_twopop and MuPoMo_main_multipop.'
+
+Keywords : 'time series, demography, mortality, population, nonlinear, optimization, non parametric
+smoothing'
+
+See also : 'MuPoMo_data, MuPoMo_normalization, MuPoMo_referencecurve, MuPoMo_main_twopop,
+MuPoMo_main_multipop, MuPoMo_bootstrap'
+
+Author : Lei Fang, Juhyun Park
+
+Submitted : Mon, June 13 2016 by Lei Fang
+
+```
+
+
+### R Code:
+```r
+optimization = function(theta, kt, kt.reference) {
+           t = time(kt)
+ t.reference = time(kt.reference)
+    
+    ### loss function
+    loss = function(theta, t, kt, t.reference, kt.reference) {
+        ## assume theta[1]>0, theta[3]>0, if not, take absolute values
+        theta1 = abs(theta[1])
+        theta2 = theta[2]
+        theta3 = abs(theta[3])
+        
+        if (theta[1] < 0 | theta[3] < 0) 
+            warning("theta1 or theta3 <0, abs value is used")
+        sm.t = (t.reference - theta2)/theta3  # time adjustment
+        ## common domain for kt and time-adjusted kt.reference
+        tmin = max(min(t), min(sm.t))
+        tmax = min(max(t), max(sm.t))
+        i0   = which(t >= tmin & t <= tmax)  # index for common domain
+        if (length(i0) > 0) {
+            t0 = t[i0]
+            ## smooth interpolation of shifted kt.reference on common grid
+            dref = data.frame(sm.t = sm.t, kt.reference = kt.reference)
+            # sm: sm.regression with optimal smoothing parameter
+            h.optimal3 = h.select(sm.t, kt.reference)
+            sm = sm.regression(sm.t, kt.reference, h = h.optimal3, eval.points = t0, model = "none", poly.index = 1, display = "none")
+            mu = theta1 * sm$estimate
+            ## mean squared error at common grid points
+            mse = mean((kt[i0] - mu)^2)  # mse of kt and the modelled one
+        } else {
+            mse = 1e+09
+        }
+        return(mse)
+    }
+    
+    ### parameter estimation with nonlinear optimization
+    conv   = 1
+    theta0 = theta
+    while (conv != 0) {
+        # check convergence
+        out    = optim(theta0, loss, gr = NULL, t, kt, t.reference, kt.reference, control = list(maxit = 1000))  # optimization
+        conv   = out$convergence
+        theta0 = out$par
+    }
+    ### constraint on theta2 (time shift parameter)
+    if (out$par[2] >= -200 & out$par[2] <= 200) 
+        temp.par = out$par else temp.par = theta
+    result = c(temp.par, out$value, out$convergence)
+    
+    ### check results on graph
+    theta  = result[1:3]
+    theta1 = abs(theta[1])
+    theta2 = theta[2]
+    theta3 = abs(theta[3])
+    
+    sm.t   = (t.reference - theta2)/theta3  # time adjustment
+    ## common grid for kt and shifted kt.reference
+    tmin   = max(min(t), min(sm.t))
+    tmax   = min(max(t), max(sm.t))
+    i0     = which(t >= tmin & t <= tmax)
+    t0     = t[i0]
+    ## shifted curves (kt.hat)
+    dref   = data.frame(sm.t = sm.t, kt.reference = kt.reference)
+    
+    # sm: sm.regression with optimal smoothing parameter
+    h.optimal4 = h.select(sm.t, kt.reference)
+    sm         = sm.regression(sm.t, kt.reference, h = h.optimal4, eval.points = sm.t, model = "none", poly.index = 1, display = "none")
+    mu         = theta1 * sm$estimate
+    mu         = ts(mu, start = sm.t[1], frequency = theta3)
+    
+    # sm: sm.regression with optimal smoothing parameter
+    h.optimal5 = h.select(sm.t, kt.reference)
+    sm0        = sm.regression(sm.t, kt.reference, h = h.optimal5, eval.points = t0, model = "none", poly.index = 1, display = "none")
+    mu0        = theta1 * sm0$estimate
+    mu0        = ts(mu0, start = t0[1], frequency = 1)
+    
+    return(list(result, mu, mu0, tmin, tmax))
+}
+
+```

From c4087e45e01893fa282e27445c7436ae0590ed78 Mon Sep 17 00:00:00 2001
From: Lukas Borke <admin@quantnet.technology>
Date: Fri, 9 Dec 2016 15:03:32 +0100
Subject: [PATCH 35/63] auto create md

---
 MuPoMo_referencecurve/README.md | 51 +++++++++++++++++++++++++++++++++
 1 file changed, 51 insertions(+)
 create mode 100644 MuPoMo_referencecurve/README.md

diff --git a/MuPoMo_referencecurve/README.md b/MuPoMo_referencecurve/README.md
new file mode 100644
index 0000000..9d30b61
--- /dev/null
+++ b/MuPoMo_referencecurve/README.md
@@ -0,0 +1,51 @@
+
+[<img src="https://github.com/QuantLet/Styleguide-and-FAQ/blob/master/pictures/banner.png" width="888" alt="Visit QuantNet">](http://quantlet.de/)
+
+## [<img src="https://github.com/QuantLet/Styleguide-and-FAQ/blob/master/pictures/qloqo.png" alt="Visit QuantNet">](http://quantlet.de/) **MuPoMo_referencecurve** [<img src="https://github.com/QuantLet/Styleguide-and-FAQ/blob/master/pictures/QN2.png" width="60" alt="Visit QuantNet 2.0">](http://quantlet.de/)
+
+```yaml
+
+Name of QuantLet : MuPoMo_referencecurve
+
+Published in : MuPoMo
+
+Description : 'Regenerates reference curve (common trend) based on normalized optimal theta
+parameters and smoothed original kt, and will be called in MuPoMo_main_multipop.'
+
+Keywords : time series, demography, mortality, population, normalization
+
+See also : 'MuPoMo_data, MuPoMo_optimization, MuPoMo_normalization, MuPoMo_main_twopop,
+MuPoMo_main_multipop, MuPoMo_bootstrap'
+
+Author : Lei Fang
+
+Submitted : Mon, June 13 2016 by Lei Fang
+
+```
+
+
+### R Code:
+```r
+referencecurve  = function(theta2, theta3, kt, kt.null) {
+    t           = time(kt)
+    sm.t        = theta3 * t + theta2  # time adjustment
+    t.reference = Sweden$year
+    ## common grid for kt and shifted kt.reference
+    tmin = max(min(t.reference), min(sm.t))
+    tmax = min(max(t.reference), max(sm.t))
+    i0   = which(t.reference >= tmin & t.reference <= tmax)
+    if (length(i0) > 0) {
+        t0  = t.reference[i0]
+        d   = data.frame(kt, sm.t)
+        # sm: sm.regression with optimal smoothing parameter
+        h.optimal6 = h.select(sm.t, kt)
+        sm  = sm.regression(sm.t, kt, h = h.optimal6, eval.points = t0, model = "none", poly.index = 1, display = "none")
+        mu1 = sm$estimate
+        mu  = ts(mu1, start = t0[1], frequency = 1)
+    } else {
+        mu  = kt.null
+    }
+    return(mu)
+}
+
+```

From 8c18c0115cd12f16900aeeeea0ecb888043c5e83 Mon Sep 17 00:00:00 2001
From: StefanGam <154674303+StefanGam@users.noreply.github.com>
Date: Thu, 19 Dec 2024 23:39:57 +0200
Subject: [PATCH 36/63] Delete existing MuPoMo_bootstrap/README.md

---
 MuPoMo_bootstrap/README.md | 240 -------------------------------------
 1 file changed, 240 deletions(-)
 delete mode 100644 MuPoMo_bootstrap/README.md

diff --git a/MuPoMo_bootstrap/README.md b/MuPoMo_bootstrap/README.md
deleted file mode 100644
index 92f8a4c..0000000
--- a/MuPoMo_bootstrap/README.md
+++ /dev/null
@@ -1,240 +0,0 @@
-
-[<img src="https://github.com/QuantLet/Styleguide-and-FAQ/blob/master/pictures/banner.png" width="888" alt="Visit QuantNet">](http://quantlet.de/)
-
-## [<img src="https://github.com/QuantLet/Styleguide-and-FAQ/blob/master/pictures/qloqo.png" alt="Visit QuantNet">](http://quantlet.de/) **MuPoMo_bootstrap** [<img src="https://github.com/QuantLet/Styleguide-and-FAQ/blob/master/pictures/QN2.png" width="60" alt="Visit QuantNet 2.0">](http://quantlet.de/)
-
-```yaml
-
-Name of QuantLet : MuPoMo_bootstrap
-
-Published in : MuPoMo
-
-Description : 'Forecasts mortality rates based on a semi-parametric approach, and bootstraps time
-series with innovation to compute the prediction intervals. Uses random two countries to
-demonstrate.'
-
-Keywords : 'time series, demography, mortality, population, nonparametric smoothing, parametric
-modelling, Lee-Carter method, bootstrap'
-
-See also : 'MuPoMo_data, MuPoMo_optimization, MuPoMo_normalization, MuPoMo_referencecurve,
-MuPoMo_main_twopop, MuPoMo_main_multipop'
-
-Author : Lei Fang
-
-Submitted : Mon, June 13 2016 by Lei Fang
-
-Example : Prediction intervals at different levels, Histogram of theta1
-
-```
-
-![Picture1](Histogram of theta1.png)
-
-![Picture2](Prediction intervals at different levels.png)
-
-
-### R Code:
-```r
-# clear history and close windows
-rm(list=ls(all=TRUE))
-graphics.off()
-
-# please set working directory
-# setwd("C:/...")     # windows
-# setwd("/Users/...") # mac os
-# setwd("~/...")      # linux
-
-# install packages
-library(demography)
-library(rgl)
-library(sm)
-library(boot)
-library(tseries)
-
-# setting
-par(mar = c(5, 5, 2, 2), cex.axis = 1.5, cex.lab = 2)
-options(digits = 4)
-
-# load saved RData to reduce code-running time from previous procedure (MuPoMo_main_multipop.R)
-# load("~/.../MuPoMo_main_multipop.RData")
-
-# Bootstrap to resample from China's mortality time series to construct the CI for shape deviation parameters theta
-
-# Reference time series curve (unchanged). We use for comparing with resampled Japan's mortality TS
-kt.referencet = reference4
-# Original Japan's mortality TS, from which we are going to take TS bootstrap
-boot.data     = kt.Japan.female
-# Initialize theta values for optimazation
-theta         = theta4[16, ]
-
-### loss function
-loss = function(theta, t, kt, t.reference, kt.reference) {
-    ## assume theta[1]>0, theta[3]>0, if not, take absolute values
-    theta1 = abs(theta[1])
-    theta2 = theta[2]
-    theta3 = abs(theta[3])
-    
-    if (theta[1] < 0 | theta[3] < 0) 
-        warning("theta1 or theta3 <0, abs value is used")
-    # time adjustment
-    sm.t = (t.reference - theta2)/theta3  
-    ## common domain for kt and time-adjusted kt.reference
-    tmin = max(min(t), min(sm.t))
-    tmax = min(max(t), max(sm.t))
-    # index for common domain
-    i0 = which(t >= tmin & t <= tmax)
-    
-    if (length(i0) > 0) {
-        t0 = t[i0]
-        ## smooth interpolation of shifted kt.reference on common grid
-        dref = data.frame(sm.t = sm.t, kt.reference = kt.reference)
-        
-        # sm: sm.regression with optimal smoothing parameter 
-        h.optimal3 = h.select(sm.t, kt.reference) 
-        sm = sm.regression(sm.t, kt.reference, h = h.optimal3, eval.points = t0, model = 'none', poly.index = 1, display = 'none') 
-        mu = theta1 * sm$estimate
-
-        ## mean squared error at common grid points
-        mse = mean((kt[i0] - mu)^2)  # mse of kt and the modelled one
-    } else {
-        mse = 1e+09
-    }
-    return(mse)
-}
-
-# Construct the 'statistic' function which is needed and very important in 'tsboot' tsboot (tseries, statistic, R, l = NULL, sim =
-# 'model',...)
-boot.func = function(kt) {
-    t = time(kt)
-    t.reference = time(kt.reference)
-    ### parameter estimation
-    conv   = 1
-    theta0 = theta
-    while (conv != 0) {
-        # check convergence
-        out    = optim(theta0, loss, gr = NULL, t, kt, t.reference, kt.reference, control = list(maxit = 1000))  # optimization
-        conv   = out$convergence
-        theta0 = out$par
-    }
-    # add constraint on theta2
-    if (out$par[2] >= -200 & out$par[2] <= 200) 
-        temp.par = out$par else temp.par = theta
-    result = c(temp.par, out$value, out$convergence)
-}
-
-# simulate time series with innovation
-bootdata.fit = auto.arima(boot.data)
-sim = 500
-plot(boot.data, xlab = "Time", ylab = "Kt", ylim = c(-150, 70), col = "blue", lwd = 10)
-
-for (i in 1:sim) {
-    nam5  = paste("sim.ts", i, sep = ".")
-    # simulate time seriese based on bootstrap of innovation/error term in ARIMA fitting model
-    temp5 = simulate(bootdata.fit, nsim = length(boot.data), future = FALSE, bootstrap = TRUE)
-    assign(nam5, temp5)
-    # time series test on plot
-    lines(temp5, col = "grey")
-}
-
-# compute parameters theta's based on bootstrapped time series
-theta.boot = matrix(rep(c(0, 0, 0, 0, 0), sim), sim, 5, byrow = TRUE)
-
-for (i in 1:sim) {
-    theta.boot[i, ] = boot.func(eval(parse(text = paste("sim.ts", i, sep = "."))))
-}
-
-# plot test
-hist(theta.boot[, 1], xlab = "theta 1", main = "Histogram of theta 1")
-quantile(theta.boot[, 1])
-
-hist(theta.boot[, 2][which(theta.boot[, 2] >= -100 & theta.boot[, 2] <= 100)], xlab = "theta 2", 
-     main = "Histogram of theta 2", xlim = c(-5, 5), breaks = 10)
-quantile(theta.boot[, 2])
-
-hist(theta.boot[, 3][which(theta.boot[, 3] >= 0.8 & theta.boot[, 3] <= 1.2)], xlab = "theta 3", 
-     main = "Histogram of theta 3", xlim = c(0.93, 0.99), breaks = 10)
-quantile(theta.boot[, 3])
-
-# forecast with estimated parameters from bootstrap
-boot.forecast = function(theta, kt, kt.reference) {
-    t = time(kt)
-    t.reference = time(kt.reference)
-    ### check results on graph
-    theta1 = abs(theta[1])
-    theta2 = theta[2]
-    theta3 = abs(theta[3])
-    # time adjustment
-    sm.t = (t.reference - theta2)/theta3
-    ## common grid for kt and shifted kt.reference
-    tmin = max(min(t), min(sm.t))
-    tmax = min(max(t), max(sm.t))
-    i0   = which(t >= tmin & t <= tmax)
-    t0   = t[i0]
-    ## shifted curves (kt.hat)
-    dref = data.frame(sm.t = sm.t, kt.reference = kt.reference)
-    # sm: sm.regression with optimal smoothing parameter
-    h.optimal4 = h.select(sm.t, kt.reference)
-    sm = sm.regression(sm.t, kt.reference, h = h.optimal4, eval.points = sm.t, model = "none", poly.index = 1, display = "none")
-    mu = theta1 * sm$estimate
-
-    mu = ts(mu, start = sm.t[1], frequency = theta3)
-    
-    # sm: sm.regression with optimal smoothing parameter
-    h.optimal5 = h.select(sm.t, kt.reference)
-    sm0 = sm.regression(sm.t, kt.reference, h = h.optimal5, eval.points = t0, model = "none", poly.index = 1, display = "none")
-    mu0 = theta1 * sm0$estimate
-
-    mu0 = ts(mu0, start = t0[1], frequency = 1)
-    
-    return(list(mu, mu0, tmin, tmax))
-}
-
-# forecast
-plot(forecast(bootdata.fit, h = 40, level = 95), xlab = "Time", ylab = "Kt", xlim = c(1828, 2050), ylim = c(-200, 150))
-lines(kt.referencet, col = "blue", lwd = 5)
-lines(boot.data, col = "red", lwd = 5)
-
-for (i in 1:sim) {
-    temp  = boot.forecast(theta.boot[i, 1:3], boot.data, kt.reference)
-    nam12 = paste("shift.kt.boot", i, sep = ".")
-    assign(nam12, temp[[2]])
-    nam15 = paste("mu.boot", i, sep = ".")
-    assign(nam15, temp[[1]])
-    lines(temp[[2]], col = "green")  
-    lines(temp[[1]], col = "grey")  
-}
-
-# prediction interval
-for (i in 2010:2050) {
-    nam = matrix(0, 1, 500)
-    for (j in 1:sim) {
-        if (max(time(eval(parse(text = paste("mu.boot", j, sep = "."))))) >= i) 
-            nam[j] = window(eval(parse(text = paste("mu.boot", j, sep = "."))), i)[1] else nam[j] = NA
-    }
-    nam1 = paste("ts", i, sep = ".")
-    assign(nam1, nam)
-    nam2 = paste("ts", i, 5, sep = ".")
-    assign(nam2, quantile(nam, probs = seq(0, 1, 0.05), na.rm = T)[2])
-    nam3 = paste("ts", i, 95, sep = ".")
-    assign(nam3, quantile(nam, probs = seq(0, 1, 0.05), na.rm = T)[20])
-    nam4 = paste("ts", i, 20, sep = ".")
-    assign(nam4, quantile(nam, probs = seq(0, 1, 0.05), na.rm = T)[5])
-    nam5 = paste("ts", i, 80, sep = ".")
-    assign(nam5, quantile(nam, probs = seq(0, 1, 0.05), na.rm = T)[17])
-}
-
-for (j in c(5, 20, 80, 95)) {
-    ts.temp = ts(0, start = 2010, end = 2040, frequency = 1)
-    for (i in 2010:2040) {
-        ts.temp[i - 2009] = eval(parse(text = paste("ts", i, j, sep = ".")))
-    }
-    nam6 = paste("ts.forecast", j, sep = ".")
-    assign(nam6, ts.temp)
-}
-
-# plot
-plot(boot.data, lwd = 5, xlab = "Time", ylab = "Kt", xlim = c(1828, 2050), ylim = c(-200, 150))
-polygon(c(2010:2040, rev(2010:2040)), c(ts.forecast.5, rev(ts.forecast.95)), col = "yellow", border = FALSE)
-polygon(c(2010:2040, rev(2010:2040)), c(ts.forecast.20, rev(ts.forecast.80)), col = "Gray", border = FALSE)
-lines(kt.referencet, col = "blue", lwd = 5)
-lines(mu.China.4, col = 5, lty = 2, lwd = 4)
-```

From cf86e7cf30b59a79f276322f5b1c46ca9b19e21d Mon Sep 17 00:00:00 2001
From: StefanGam <154674303+StefanGam@users.noreply.github.com>
Date: Thu, 19 Dec 2024 23:40:00 +0200
Subject: [PATCH 37/63] Create README.md in folder

---
 MuPoMo_bootstrap/README.md | 32 ++++++++++++++++++++++++++++++++
 1 file changed, 32 insertions(+)
 create mode 100644 MuPoMo_bootstrap/README.md

diff --git a/MuPoMo_bootstrap/README.md b/MuPoMo_bootstrap/README.md
new file mode 100644
index 0000000..3cb3482
--- /dev/null
+++ b/MuPoMo_bootstrap/README.md
@@ -0,0 +1,32 @@
+<div style="margin: 0; padding: 0; text-align: center; border: none;">
+<a href="https://quantlet.com" target="_blank" style="text-decoration: none; border: none;">
+<img src="https://github.com/StefanGam/test-repo/blob/main/quantlet_design.png?raw=true" alt="Header Image" width="100%" style="margin: 0; padding: 0; display: block; border: none;" />
+</a>
+</div>
+
+```
+Name of QuantLet: MuPoMo_bootstrap
+
+Published in: MuPoMo
+
+Description: 'Forecasts mortality rates based on a semi-parametric approach, and bootstraps time series with innovation to compute the prediction intervals. Uses random two countries to demonstrate.'
+
+Keywords: 'time series, demography, mortality, population, nonparametric smoothing, parametric modelling, Lee-Carter method,
+
+See also: 'MuPoMo_data, MuPoMo_optimization, MuPoMo_normalization,
+
+Author: Lei Fang
+
+Submitted: Mon, June 13 2016 by Lei Fang
+
+Example: 
+
+```
+<div align="center">
+<img src="https://raw.githubusercontent.com/QuantLet/MuPoMo/master/MuPoMo_bootstrap/Histogram%20of%20theta1.png" alt="Image" />
+</div>
+
+<div align="center">
+<img src="https://raw.githubusercontent.com/QuantLet/MuPoMo/master/MuPoMo_bootstrap/Prediction%20intervals%20at%20different%20levels.png" alt="Image" />
+</div>
+

From 105ac14fa48f8d50842e675bfb08792973616dd3 Mon Sep 17 00:00:00 2001
From: StefanGam <154674303+StefanGam@users.noreply.github.com>
Date: Thu, 19 Dec 2024 23:40:03 +0200
Subject: [PATCH 38/63] Delete existing MuPoMo_data/README.md

---
 MuPoMo_data/README.md | 59 -------------------------------------------
 1 file changed, 59 deletions(-)
 delete mode 100644 MuPoMo_data/README.md

diff --git a/MuPoMo_data/README.md b/MuPoMo_data/README.md
deleted file mode 100644
index 6c88804..0000000
--- a/MuPoMo_data/README.md
+++ /dev/null
@@ -1,59 +0,0 @@
-
-[<img src="https://github.com/QuantLet/Styleguide-and-FAQ/blob/master/pictures/banner.png" width="888" alt="Visit QuantNet">](http://quantlet.de/)
-
-## [<img src="https://github.com/QuantLet/Styleguide-and-FAQ/blob/master/pictures/qloqo.png" alt="Visit QuantNet">](http://quantlet.de/) **MuPoMo_data** [<img src="https://github.com/QuantLet/Styleguide-and-FAQ/blob/master/pictures/QN2.png" width="60" alt="Visit QuantNet 2.0">](http://quantlet.de/)
-
-```yaml
-
-Name of QuantLet : MuPoMo_data
-
-Published in : MuPoMo
-
-Description : 'Reads data from Human Mortality Database and calculate kt, and will be called in
-MuPoMo_main_twopop and MuPoMo_main_multipop.'
-
-Keywords : 'time series, demography, mortality, Lee-Carter method, population, Human Mortality
-Database'
-
-See also : 'MuPoMo_optimization, MuPoMo_normalization, MuPoMo_referencecurve, MuPoMo_main_twopop,
-MuPoMo_main_multipop, MuPoMo_bootstrap'
-
-Author : Lei Fang
-
-Submitted : Mon, June 13 2016 by Lei Fang
-
-```
-
-
-### R Code:
-```r
-# read multi-pop female mortality rates from Human Mortality Database
-shortnames.all = c("AUS", "AUT", "BLR", "BGR", "CAN", "CHL", "CZE", "DNK", "EST", "FIN", "FRATNP", "DEUTNP", "HUN", "ISL", "IRL", 
-    "ISR", "ITA", "JPN", "LVA", "LTU", "LUX", "NLD", "NZL_NP", "NOR", "POL", "PRT", "RUS", "SVK", "SVN", "ESP", "CHE", "TWN", "GBR_NP", 
-    "USA", "SWE")
-names.all = c("Australia", "Austria", "Belarus", "Bulgaria", "Canada", "Chile", "CzechRepublic", "Denmark", "Estonia", "Finland", 
-    "France", "Germany", "Hungary", "Iceland", "Ireland", "Israel", "Italy", "Japan", "Latvia", "Lithuania", "Luxembourg", "Netherlands", 
-    "NewZealand", "Norway", "Poland", "Portugal", "Russia", "Slovakia", "Slovenia", "Spain", "Switzerland", "Taiwan", "UnitedKingdom", 
-    "USA", "Sweden")
-
-loop.all = length(names.all)
-for (i in 1:loop.all) {
-    nam1 = paste(names.all[i])
-    # read data from Human Mortality Database (HMD: http://www.mortality.org/)
-    # you need register on HMD to access a free account accound and set up your password
-    assign(nam1, hmd.mx(shortnames.all[i], "account", "password", names.all[i]))
-    temp1 = hmd.mx(shortnames.all[i], "account", "password", names.all[i])
-    nam2  = paste(names.all[i], "lca.female", sep = ".")
-    # Lee-Carter method
-    assign(nam2, lca(temp1, series = "female", adjust = "dt", interpolate = TRUE))
-    temp2 = lca(temp1, series = "female", adjust = "dt", interpolate = TRUE)
-    nam3  = paste("ax", names.all[i], "female", sep = ".")  # ax
-    assign(nam3, temp2$ax)
-    nam4  = paste("bx", names.all[i], "female", sep = ".")  # bx
-    assign(nam4, temp2$bx)
-    nam5  = paste("kt", names.all[i], "female", sep = ".")  # kt
-    assign(nam5, temp2$kt)
-}
-
-
-```

From c0d42fae922b69621208bb7d87405e4798784461 Mon Sep 17 00:00:00 2001
From: StefanGam <154674303+StefanGam@users.noreply.github.com>
Date: Thu, 19 Dec 2024 23:40:05 +0200
Subject: [PATCH 39/63] Create README.md in folder

---
 MuPoMo_data/README.md | 22 ++++++++++++++++++++++
 1 file changed, 22 insertions(+)
 create mode 100644 MuPoMo_data/README.md

diff --git a/MuPoMo_data/README.md b/MuPoMo_data/README.md
new file mode 100644
index 0000000..69d07dc
--- /dev/null
+++ b/MuPoMo_data/README.md
@@ -0,0 +1,22 @@
+<div style="margin: 0; padding: 0; text-align: center; border: none;">
+<a href="https://quantlet.com" target="_blank" style="text-decoration: none; border: none;">
+<img src="https://github.com/StefanGam/test-repo/blob/main/quantlet_design.png?raw=true" alt="Header Image" width="100%" style="margin: 0; padding: 0; display: block; border: none;" />
+</a>
+</div>
+
+```
+Name of QuantLet: MuPoMo_data
+
+Published in: MuPoMo
+
+Description: 'Reads data from Human Mortality Database and calculate kt, and will be called
+
+Keywords: 'time series, demography, mortality, Lee-Carter method, population, Human Mortality Database'
+
+See also: 'MuPoMo_optimization, MuPoMo_normalization, MuPoMo_referencecurve,
+
+Author: Lei Fang
+
+Submitted: Mon, June 13 2016 by Lei Fang
+
+```

From edf00237c78a5b8a63b743108efe70912a35fae0 Mon Sep 17 00:00:00 2001
From: StefanGam <154674303+StefanGam@users.noreply.github.com>
Date: Thu, 19 Dec 2024 23:40:07 +0200
Subject: [PATCH 40/63] Delete existing MuPoMo_main_multipop/README.md

---
 MuPoMo_main_multipop/README.md | 192 ---------------------------------
 1 file changed, 192 deletions(-)
 delete mode 100644 MuPoMo_main_multipop/README.md

diff --git a/MuPoMo_main_multipop/README.md b/MuPoMo_main_multipop/README.md
deleted file mode 100644
index 5156cc8..0000000
--- a/MuPoMo_main_multipop/README.md
+++ /dev/null
@@ -1,192 +0,0 @@
-
-[<img src="https://github.com/QuantLet/Styleguide-and-FAQ/blob/master/pictures/banner.png" width="888" alt="Visit QuantNet">](http://quantlet.de/)
-
-## [<img src="https://github.com/QuantLet/Styleguide-and-FAQ/blob/master/pictures/qloqo.png" alt="Visit QuantNet">](http://quantlet.de/) **MuPoMo_main_multipop** [<img src="https://github.com/QuantLet/Styleguide-and-FAQ/blob/master/pictures/QN2.png" width="60" alt="Visit QuantNet 2.0">](http://quantlet.de/)
-
-```yaml
-
-Name of QuantLet : MuPoMo_main_multipop
-
-Published in : MuPoMo
-
-Description : 'Estimates and forecasts mortality rates based on a semi-parametric approach, which
-applies parametric modelling for multiple nonparametric smoothed curves with the shape-related
-nonlinear variation.'
-
-Keywords : 'time series, demography, mortality, population, nonparametric smoothing, parametric
-modelling, Lee-Carter method'
-
-See also : 'MuPoMo_data, MuPoMo_optimization, MuPoMo_normalization, MuPoMo_referencecurve,
-MuPoMo_main_twopop, MuPoMo_bootstrap'
-
-Author : Lei Fang
-
-Submitted : Mon, June 13 2016 by Lei Fang
-
-Example : Multi-Population model with German data, Multi-Population model with Japanese data
-
-```
-
-![Picture1](Multi-Population model with German data.png)
-
-![Picture2](Multi-Population model with Japanese data.png)
-
-
-### R Code:
-```r
-# clear history and close windows
-rm(list=ls(all=TRUE))
-graphics.off()
-
-# please set working directory
-# setwd("C:/...")     # windows
-# setwd("/Users/...") # mac os
-# setwd("~/...")      # linux
-
-# install packages
-library(demography)
-library(rgl)
-library(sm)
-
-# set plot
-par(mar = c(5, 5, 2, 2), cex.axis = 1.5, cex.lab = 2)
-
-# recall self-defined functions
-source('MuPoMo_data.R')
-source("MuPoMo_optimization.R")
-source("MuPoMo_normalization.R")
-source("MuPoMo_referencecurve.R")
-
-# set bandwidth
-bw.default = 2.5
-
-## descriptive plot plot kt of 35 countries
-plot(kt.Sweden.female, type = "l", ylim = c(-250, 150), xlab = "Time", ylab = "kt", main = "Original Kt (35 countries)")
-for (i in 1:(loop.all - 1)) {
-    lines(eval(parse(text  = paste("kt.", names.all[i], ".female", sep = ""))), col = i)
-}
-
-##### common trend
-#### initial setting nonparametric smoothing 35 countries
-for (i in 1:loop.all) {
-    kt = eval(parse(text = paste("kt.", names.all[i], ".female", sep = "")))
-    t  = eval(parse(text = paste(names.all[i])))$year
-    d  = data.frame(kt, t)
-    # sm: sm.regression with optimal smoothing parameter
-    h.optimal1 = h.select(t, kt)
-    sm         = sm.regression(t, kt, h = h.optimal1, eval.points = t, model = "none", poly.index = 1, display = "none")
-    nam6       = paste("sm.kt", names.all[i], "female", sep = ".")
-    temp6      = ts(sm$estimate, start = t[1], frequency = 1)
-    assign(nam6, temp6)
-}
-
-## plot smoothed kt of 35 countries
-plot(sm.kt.Sweden.female, type = "l", ylim = c(-250, 150), xlab = "Time", ylab = "kt", main = "Smoothed Kt (35 countries)")
-for (i in 1:(loop.all - 1)) {
-    lines(eval(parse(text = paste("sm.kt.", names.all[i], ".female", sep = ""))), col = i)
-}
-
-#### intial values of thetas 
-### remove Russia, Lithuavia, Latvia, Estonia and Belarus 
-### set up the initial reference curve based on 31 countries
-names.31 = c("Australia", "Austria", "Bulgaria", "Canada", "Chile", "CzechRepublic", "Denmark", "Finland", "France", "Germany", "Hungary", 
-    "Iceland", "Ireland", "Israel", "Italy", "Japan", "Luxembourg", "Netherlands", "NewZealand", "Norway", "Poland", "Portugal", "Slovakia", 
-    "Slovenia", "Spain", "Switzerland", "Taiwan", "UnitedKingdom", "USA", "Sweden")
-loop.31  = length(names.31)
-merge1   = sm.kt.Australia.female
-for (i in 1:(loop.31 - 1)) {
-    nam7  = paste("merge", i + 1, sep = "")
-    temp3 = merge.zoo(eval(parse(text = paste("merge", i, sep = ""))), eval(parse(text = paste("sm.kt.", names.31[i + 1], ".female", 
-        sep = ""))))
-    assign(nam7, temp3)
-}
-reference0.temp = rowMeans(merge31, na.rm = TRUE)
-reference0      = ts(reference0.temp, start = Sweden$year[1], frequency = 1)
-
-## plot the reference curve among all 31 smoothed curves
-plot(sm.kt.Sweden.female, type = "l", ylim = c(-250, 150), xlab = "Time", ylab = "kt", main = "Reference Curve vs. Smoothed Kt (31 countries)")
-for (i in 1:loop.31) {
-    lines(eval(parse(text = paste("sm.kt.", names.31[i], ".female", sep = ""))), col = i)
-}
-lines(reference0, lwd = 4, col = "red")
-
-##### begin loop
-theta0    = matrix(rep(c(1, 0, 1), loop.31), loop.31, 3, byrow = TRUE)
-iteration = 5
-for (j in 1:iteration) {
-    ### find the optimal initial theta based on the reference curve
-    theta        = eval(parse(text = paste("theta", j - 1, sep = "")))
-    kt.reference = eval(parse(text = paste("reference", j - 1, sep = "")))
-    results      = matrix(NA, loop.31, 5)  # c(theta1,theta2,theta3, loss, convergence)
-    for (i in 1:loop.31) {
-        kt           = eval(parse(text = paste("sm.kt.", names.31[i], ".female", sep = "")))
-        tt           = time(kt)
-        ltt          = length(tt)
-        temp4        = optimization(theta[i, ], kt, kt.reference)
-        results[i, ] = temp4[[1]]
-        nam12        = paste("shift.kt", names.31[i], j, sep = ".")
-        assign(nam12, temp4[[3]])
-        nam15        = paste("mu", names.31[i], j, sep = ".")
-        assign(nam15, temp4[[2]])
-        pdf(paste("plot_", j, "_", i, ".pdf", sep = ""))
-        par(mar = c(5, 5, 2, 2))
-        plot(eval(parse(text = paste("kt.", names.31[i], ".female", sep = ""))), ylim = c(-250, 150), xlim = c(1750, 2020), type = "p", 
-            xlab = "Time", ylab = "kt", main = paste(names.31[i], tt[1], "--", tt[ltt], ":step", j))
-        lines(kt, col = 2)  # sm.kt
-        lines(kt.reference, col = 4, lwd = 2)  # reference
-        lines(temp4[[2]], col = 5, lty = 5)  # new kt
-        lines(temp4[[3]], col = 5, lwd = 2)  # new kt
-        abline(v = temp4[[4]], col = "gray", lty = 5)
-        abline(v = temp4[[5]], col = "gray", lty = 5)
-        # legend('topright', legend=c('kt', 'sm.kt', 'k0', 'kt.hat'), col=c(1,2,4,5), lty=1)
-        dev.off()
-    }
-    nam16 = paste("results", j, sep = "")
-    assign(nam16, results)
-    nam18 = paste("theta", j, sep = "")
-    assign(nam18, results[, 1:3])
-    
-    ## plot shifted kt of 31 countries and the reference curve of previous step
-    plot(kt.reference, type = "l", ylim = c(-250, 150), xlab = "Time", ylab = "kt", lwd = 4, col = "red", main = paste("Reference Curve vs. Shifted Kt (31 countries): step", 
-        j - 1))
-    for (i in 1:loop.31) {
-        lines(eval(parse(text = paste("shift.kt", names.31[i], j, sep = "."))), col = i)
-    }
-    
-    # construct optimal.theta.matrix and normalize optimal theta
-    optimal.theta.matrix          = results[, 1:3]
-    standard.optimal.theta.matrix = normalization(optimal.theta.matrix)
-    
-    # construct new reference curve
-    for (i in 1:loop.31) {
-        nam13 = paste("shift.kt", names.31[i], "standard", sep = ".")
-        assign(nam13, referencecurve(standard.optimal.theta.matrix[i, 2], standard.optimal.theta.matrix[i, 3], eval(parse(text = paste("sm.kt.", 
-            names.31[i], ".female", sep = ""))), eval(parse(text = paste("shift.kt", names.31[i], j, sep = ".")))))
-    }
-    merge1.1  = shift.kt.Australia.standard
-    for (i in 1:(loop.31 - 1)) {
-        nam7  = paste("merge1", i + 1, sep = ".")
-        temp3 = merge.zoo(eval(parse(text = paste("merge1", i, sep = "."))), eval(parse(text = paste("shift.kt", names.31[i + 1], 
-            "standard", sep = "."))))
-        assign(nam7, temp3)
-    }
-    reference.temp           = rowMeans(merge1.31, na.rm = TRUE)
-    reference.temp.nonsmooth = ts(reference.temp, start = min(index(merge1.31)), frequency = 1)
-    t.temp                   = time(reference.temp.nonsmooth)
-    
-    ## smooth the updated reference curve
-    # sm: sm.regression
-    temp17 = sm.regression(t.temp, reference.temp.nonsmooth, eval.points = t.temp, model = "none", poly.index = 1, display = "none")
-    nam17  = paste("reference", j, sep = "")
-    assign(nam17, ts(temp17$estimate, start = t.temp[1], frequency = 1))
-    
-    ## plot the updated reference curve among all 31 shifted curves
-    plot(eval(parse(text = paste("reference", j, sep = ""))), lwd = 4, col = "red", type = "l", ylim = c(-250, 150), xlab = "Time", 
-        ylab = "kt", main = paste("Updated Reference Curve vs. Shifted Kt (31 countries): step", j))
-    for (i in 1:loop.31) {
-        lines(eval(parse(text = paste("shift.kt", names.31[i], j, sep = "."))), col = i)
-        lines(eval(parse(text = paste("sm.kt.", names.31[i], ".female", sep = ""))), col = "grey")
-    }
-    lines(eval(parse(text = paste("reference", j - 1, sep = ""))), col = "blue", lwd = 3, lty = 5)
-}
-```

From 01baf2fba1bd3b2798f9d16c7833b15fd53f6808 Mon Sep 17 00:00:00 2001
From: StefanGam <154674303+StefanGam@users.noreply.github.com>
Date: Thu, 19 Dec 2024 23:40:09 +0200
Subject: [PATCH 41/63] Create README.md in folder

---
 MuPoMo_main_multipop/README.md | 32 ++++++++++++++++++++++++++++++++
 1 file changed, 32 insertions(+)
 create mode 100644 MuPoMo_main_multipop/README.md

diff --git a/MuPoMo_main_multipop/README.md b/MuPoMo_main_multipop/README.md
new file mode 100644
index 0000000..cab21b5
--- /dev/null
+++ b/MuPoMo_main_multipop/README.md
@@ -0,0 +1,32 @@
+<div style="margin: 0; padding: 0; text-align: center; border: none;">
+<a href="https://quantlet.com" target="_blank" style="text-decoration: none; border: none;">
+<img src="https://github.com/StefanGam/test-repo/blob/main/quantlet_design.png?raw=true" alt="Header Image" width="100%" style="margin: 0; padding: 0; display: block; border: none;" />
+</a>
+</div>
+
+```
+Name of QuantLet: MuPoMo_main_multipop
+
+Published in: MuPoMo
+
+Description: 'Estimates and forecasts mortality rates based on a semi-parametric approach, which applies parametric modelling for
+
+Keywords: 'time series, demography, mortality, population, nonparametric smoothing, parametric modelling, Lee-Carter method'
+
+See also: 'MuPoMo_data, MuPoMo_optimization, MuPoMo_normalization,
+
+Author: Lei Fang
+
+Submitted: Mon, June 13 2016 by Lei Fang
+
+Example: 
+
+```
+<div align="center">
+<img src="https://raw.githubusercontent.com/QuantLet/MuPoMo/master/MuPoMo_main_multipop/Multi-Population%20model%20with%20German%20data.png" alt="Image" />
+</div>
+
+<div align="center">
+<img src="https://raw.githubusercontent.com/QuantLet/MuPoMo/master/MuPoMo_main_multipop/Multi-Population%20model%20with%20Japanese%20data.png" alt="Image" />
+</div>
+

From 5309554be646dd13eeaac02de7467d0f7efe46a9 Mon Sep 17 00:00:00 2001
From: StefanGam <154674303+StefanGam@users.noreply.github.com>
Date: Thu, 19 Dec 2024 23:40:11 +0200
Subject: [PATCH 42/63] Delete existing MuPoMo_main_twopop/README.md

---
 MuPoMo_main_twopop/README.md | 195 -----------------------------------
 1 file changed, 195 deletions(-)
 delete mode 100644 MuPoMo_main_twopop/README.md

diff --git a/MuPoMo_main_twopop/README.md b/MuPoMo_main_twopop/README.md
deleted file mode 100644
index 44c5dd7..0000000
--- a/MuPoMo_main_twopop/README.md
+++ /dev/null
@@ -1,195 +0,0 @@
-
-[<img src="https://github.com/QuantLet/Styleguide-and-FAQ/blob/master/pictures/banner.png" width="888" alt="Visit QuantNet">](http://quantlet.de/)
-
-## [<img src="https://github.com/QuantLet/Styleguide-and-FAQ/blob/master/pictures/qloqo.png" alt="Visit QuantNet">](http://quantlet.de/) **MuPoMo_main_twopop** [<img src="https://github.com/QuantLet/Styleguide-and-FAQ/blob/master/pictures/QN2.png" width="60" alt="Visit QuantNet 2.0">](http://quantlet.de/)
-
-```yaml
-
-Name of QuantLet : MuPoMo_main_twopop
-
-Published in : MuPoMo
-
-Description : 'Estimates and forecasts mortality rates based on a semi-parametric approach, which
-applies parametric modelling for multiple nonparametric curves with the shape-related nonlinear
-variation. Uses random two countries to demonstrate two-country case.'
-
-Keywords : 'time series, demography, mortality, population, nonparametric smoothing, parametric
-modelling, Lee-Carter method, contour'
-
-See also : 'MuPoMo_data, MuPoMo_optimization, MuPoMo_normalization, MuPoMo_referencecurve,
-MuPoMo_main_multipop, MuPoMo_bootstrap'
-
-Author : Lei Fang
-
-Submitted : Mon, June 13 2016 by Lei Fang
-
-Example : 'Time shift at different levels, Loss function of theta2, Loss surface 3D, Contour plot
-of theta2 and theta4, Model fit and forecast'
-
-```
-
-![Picture1](Contour plot of theta2 and theta4.png)
-
-![Picture2](Loss function of theta2.png)
-
-![Picture3](Loss surface 3D.png)
-
-![Picture4](Model fit and forecast.png)
-
-![Picture5](Time shift at different levels.png)
-
-
-### R Code:
-```r
-# clear history and close windows
-rm(list=ls(all=TRUE))
-graphics.off()
-
-# please set working directory
-# setwd("C:/...")     # windows
-# setwd("/Users/...") # mac os
-# setwd("~/...")      # linux
-
-# install packages
-library(demography)
-library(rgl)
-library(sm)
-
-# set plot
-par(mar = c(5, 5, 2, 2), cex.axis = 1.5, cex.lab = 2)
-
-# recall self-defined functions
-# read data and compute kt based on Lee-Carter Model via source('data.R')
-source('MuPoMo_data.R')
-source("MuPoMo_optimization.R")
-
-# choose two countries' kt for this analysis
-kt1 = kt.China.female
-kt2 = kt.Japan.female
-
-# set bandwidth for smoothing curves
-bw.default     = 2.5
-
-# plot kt
-plot(kt2, type = "l", col = "blue", lwd = 4, xlab = "Time", ylab = "Kt")
-lines(kt1, col = "red", lwd = 4)
-
-# shift movement of the two smoothed countries
-t1         = 1994:2010 # differ based on the chosen country
-d1         = data.frame(time(kt1), kt1)
-h.optimal1 = h.select(time(kt1), kt1)
-sm1        = sm.regression(time(kt1), kt1, h = h.optimal1, eval.points = time(kt1), model = "none", poly.index = 1, display = "none")
-sm.kt1     = sm1$estimate  # smoothed kt1
-
-t2         = 1947:2012 # differ based on the chosen country
-d2         = data.frame(time(kt2), kt2)
-h.optimal2 = h.select(time(kt2), kt2)
-sm2        = sm.regression(time(kt2), kt2, h = h.optimal2, eval.points = time(kt2), model = "none", poly.index = 1, display = "none")
-sm.kt2     = sm2$estimate  # smoothed kt2
-
-plot(t2, sm.kt2, type = "l", col = "blue", lwd = 4, xlab = "Time", ylab = "Kt")
-lines(kt2, col = "red", lwd = 4)
-lines(t1, sm.kt1, lwd = 4)
-lines(kt1, col = "darkgreen", lwd = 4)
-lines(t2 + 20, sm.kt2, lwd = 4, lty = 2) # differ based on the chosen country
-lines(t2 + 25, sm.kt2, lwd = 4, lty = 3)
-lines(t2 + 30, sm.kt2, lwd = 4, lty = 4)
-
-# time delay
-plot(t2, sm.kt2, type = "l", col = "blue", lwd = 4, xlab = "Time", ylab = "Kt")
-lines(t1, sm.kt1, lwd = 4)
-lines(t2 + 23, sm.kt2, lwd = 4, lty = 4, col = "blue") # differ based on the chosen country
-
-# vertical shift
-plot(t2, sm.kt2, type = "l", col = "blue", lwd = 4, xlab = "Time", ylab = "Kt")
-lines(t1, sm.kt1, lwd = 4)
-lines(t2, sm.kt2 + 85, lwd = 4, lty = 4, col = "blue") # differ based on the chosen country
-
-# optimization
-theta.2pop  = c(1, -23, 1) # differ based on the chosen country
-result.2pop = optimization(theta.2pop, kt1, kt2)
-
-# plot optimized movement
-plot(t2, sm.kt2, type = "l", col = 4, lwd = 4, xlab = "Time", ylab = "Kt")
-lines(kt2, type = "p", lwd = 3)
-lines(t1, sm.kt1, lwd = 4, col = 2)
-lines(kt1, type = "p", lwd = 3)
-lines(result.2pop[[2]], col = 5, lty = 5)  #
-lines(result.2pop[[3]], col = 5, lwd = 3)  #
-abline(v = result.2pop[[4]], col = "gray", lty = 5)
-abline(v = result.2pop[[5]], col = "gray", lty = 5)
-
-# plot loss function
-loss = function(theta1, theta2, theta3, theta4, t, kt, t.reference, kt.reference) {
-    sm.t = (t.reference - theta2)/theta3  # time adjustment
-    ## common domain for kt and time-adjusted kt.reference
-    tmin = max(min(t), min(sm.t))
-    tmax = min(max(t), max(sm.t))
-    i0 = which(t >= tmin & t <= tmax)  # index for common domain
-    if (length(i0) > 0) {
-        t0 = t[i0]
-        ## smooth interpolation of shifted kt.reference on common grid
-        dref = data.frame(sm.t = sm.t, kt.reference = kt.reference)
-        # sm: sm.regression with optimal smoothing parameter
-        h.optimal3 = h.select(sm.t, kt.reference)
-        sm = sm.regression(sm.t, kt.reference, h = h.optimal3, eval.points = t0, model = "none", poly.index = 1, display = "none")
-        mu = theta1 * sm$estimate + theta4
-        ## mean squared error at common grid points
-        mse = mean((kt[i0] - mu)^2)  # mse of kt and the modelled one
-    } else {
-        mse = 1e+09
-    }
-    return(mse)
-}
-
-# plot loss function of theta2 and theta4
-vtheta2 = seq(-30, 10, len = 100) # differ based on the chosen country
-vtheta4 = seq(0, 100, len = 100) # differ based on the chosen country
-npar    = length(vtheta2)
-res     = matrix(rep(0, 10000), 100, 100)
-for (i in 1:npar) {
-    for (l in 1:npar) {
-        res[i, l] = loss(1, vtheta2[i], 1, vtheta4[l], t1, kt1, t2, kt2)
-    }
-    res[i, l] = loss(1, vtheta2[i], 1, vtheta4[l], t1, kt1, t2, kt2)
-}
-
-persp3d(vtheta2, vtheta4, res, col = "blue", xlab = "theta2", ylab = "theta4", zlab = "Loss")
-
-resnew = res * (res < 5000)
-persp3d(vtheta2, vtheta4, resnew, col = "blue", xlab = "theta2", ylab = "theta4", zlab = "Loss")
-
-# contour plot
-contour(vtheta2, vtheta4, resnew, col = rainbow(20), nlevels = 20, lwd = 1, xlim = c(-23, 0), ylim = c(0, 80))
-contour(vtheta2, vtheta4, res, col = rainbow(20), nlevels = 70, lwd = 1, xlim = c(-23, 0), ylim = c(0, 80), zlim = c(0, 100))
-contour(vtheta2, vtheta4, res, col = rainbow(20), nlevels = 70, lwd = 1, xlim = c(-10, -2), ylim = c(40, 80), zlim = c(0, 100))
-
-# plot loss function of theta2
-vtheta22 = seq(-50, 0, len = 100) # differ based on the chosen country
-npar2    = length(vtheta22)
-res2     = rep(0, 100)
-for (i in 1:npar2) {
-    res2[i] = loss(1, vtheta22[i], 1, 0, t1, kt1, t2, kt2)
-}
-plot(vtheta22, res2, col = "blue", xlab = "theta2", ylab = "Loss", type = "l", lwd = 4)
-
-# plot loss function of theta4
-vtheta42 = seq(40, 140, len = 100) # differ based on the chosen country
-npar3    = length(vtheta42)
-res3     = rep(0, 100)
-for (i in 1:npar3) {
-    res3[i] = loss(1, 0, 1, vtheta42[i], t1, kt1, t2, kt2)
-}
-plot(vtheta42, res3, col = "blue", xlab = "theta4", ylab = "Loss", type = "l", lwd = 4)
-
-# forecast
-plot(t2, sm.kt2, type = "l", col = 4, lwd = 4, xlab = "Time", ylab = "Kt", xlim = c(1947, 2035))
-lines(kt2, type = "p", lwd = 3)
-lines(t1, sm.kt1, lwd = 4, col = 2)
-lines(kt1, type = "p", lwd = 3)
-lines(result.2pop[[2]], col = 4, lty = 5, lwd = 3)  #
-lines(result.2pop[[3]], col = "purple", lwd = 3)  #
-abline(v = result.2pop[[4]], col = "gray", lty = 5)
-abline(v = result.2pop[[5]], col = "gray", lty = 5)
-
-```

From 7c8373e3c31f130839eca760cdca9756c6a1b79b Mon Sep 17 00:00:00 2001
From: StefanGam <154674303+StefanGam@users.noreply.github.com>
Date: Thu, 19 Dec 2024 23:40:14 +0200
Subject: [PATCH 43/63] Create README.md in folder

---
 MuPoMo_main_twopop/README.md | 44 ++++++++++++++++++++++++++++++++++++
 1 file changed, 44 insertions(+)
 create mode 100644 MuPoMo_main_twopop/README.md

diff --git a/MuPoMo_main_twopop/README.md b/MuPoMo_main_twopop/README.md
new file mode 100644
index 0000000..4f6e122
--- /dev/null
+++ b/MuPoMo_main_twopop/README.md
@@ -0,0 +1,44 @@
+<div style="margin: 0; padding: 0; text-align: center; border: none;">
+<a href="https://quantlet.com" target="_blank" style="text-decoration: none; border: none;">
+<img src="https://github.com/StefanGam/test-repo/blob/main/quantlet_design.png?raw=true" alt="Header Image" width="100%" style="margin: 0; padding: 0; display: block; border: none;" />
+</a>
+</div>
+
+```
+Name of QuantLet: MuPoMo_main_twopop
+
+Published in: MuPoMo
+
+Description: 'Estimates and forecasts mortality rates based on a semi-parametric approach, which applies parametric modelling for
+
+Keywords: 'time series, demography, mortality, population, nonparametric smoothing, parametric modelling, Lee-Carter method,
+
+See also: 'MuPoMo_data, MuPoMo_optimization, MuPoMo_normalization,
+
+Author: Lei Fang
+
+Submitted: Mon, June 13 2016 by Lei Fang
+
+Example: 
+
+```
+<div align="center">
+<img src="https://raw.githubusercontent.com/QuantLet/MuPoMo/master/MuPoMo_main_twopop/Contour%20plot%20of%20theta2%20and%20theta4.png" alt="Image" />
+</div>
+
+<div align="center">
+<img src="https://raw.githubusercontent.com/QuantLet/MuPoMo/master/MuPoMo_main_twopop/Loss%20function%20of%20theta2.png" alt="Image" />
+</div>
+
+<div align="center">
+<img src="https://raw.githubusercontent.com/QuantLet/MuPoMo/master/MuPoMo_main_twopop/Loss%20surface%203D.png" alt="Image" />
+</div>
+
+<div align="center">
+<img src="https://raw.githubusercontent.com/QuantLet/MuPoMo/master/MuPoMo_main_twopop/Model%20fit%20and%20forecast.png" alt="Image" />
+</div>
+
+<div align="center">
+<img src="https://raw.githubusercontent.com/QuantLet/MuPoMo/master/MuPoMo_main_twopop/Time%20shift%20at%20different%20levels.png" alt="Image" />
+</div>
+

From 200954afebb18c2d60a1ebc86e2d32745701c27a Mon Sep 17 00:00:00 2001
From: StefanGam <154674303+StefanGam@users.noreply.github.com>
Date: Thu, 19 Dec 2024 23:40:16 +0200
Subject: [PATCH 44/63] Delete existing MuPoMo_normalization/README.md

---
 MuPoMo_normalization/README.md | 50 ----------------------------------
 1 file changed, 50 deletions(-)
 delete mode 100644 MuPoMo_normalization/README.md

diff --git a/MuPoMo_normalization/README.md b/MuPoMo_normalization/README.md
deleted file mode 100644
index a68dbef..0000000
--- a/MuPoMo_normalization/README.md
+++ /dev/null
@@ -1,50 +0,0 @@
-
-[<img src="https://github.com/QuantLet/Styleguide-and-FAQ/blob/master/pictures/banner.png" width="888" alt="Visit QuantNet">](http://quantlet.de/)
-
-## [<img src="https://github.com/QuantLet/Styleguide-and-FAQ/blob/master/pictures/qloqo.png" alt="Visit QuantNet">](http://quantlet.de/) **MuPoMo_normalization** [<img src="https://github.com/QuantLet/Styleguide-and-FAQ/blob/master/pictures/QN2.png" width="60" alt="Visit QuantNet 2.0">](http://quantlet.de/)
-
-```yaml
-
-Name of QuantLet : MuPoMo_normalization
-
-Published in : MuPoMo
-
-Description : 'Normalizes optimal shape variation parameters theta estimated from
-MuPoMo_optimization, and will be called in MuPoMo_main_multipop.'
-
-Keywords : time series, demography, mortality, population, normalization
-
-See also : 'MuPoMo_data, MuPoMo_optimization, MuPoMo_referencecurve, MuPoMo_main_twopop,
-MuPoMo_main_multipop, MuPoMo_bootstrap'
-
-Author : Lei Fang
-
-Submitted : Mon, June 13 2016 by Lei Fang
-
-```
-
-
-### R Code:
-```r
-normalization  = function(theta) {
-    theta.temp = colSums(theta)
-    for (i in 1:loop.31) {
-        nam10  = paste("normal.theta", names.31[i], 1, sep = ".")
-        assign(nam10, loop.31 * theta[i, 1]/theta.temp[1])
-        nam11  = paste("normal.theta", names.31[i], 3, sep = ".")
-        assign(nam11, loop.31 * theta[i, 3]/theta.temp[3])
-        nam12  = paste("normal.theta", names.31[i], 2, sep = ".")
-        assign(nam12, theta[i, 2] - theta.temp[2]/loop.31)
-        nam14  = paste("normal.theta", names.31[i], sep = ".")
-        assign(nam14, c(eval(parse(text = paste("normal.theta", names.31[i], 1, sep = "."))), eval(parse(text = paste("normal.theta", 
-            names.31[i], 2, sep = "."))), eval(parse(text = paste("normal.theta", names.31[i], 3, sep = ".")))))
-    }
-    ll = list()
-    for (i in 1:loop.31) {
-        ll[[i]]  = c(eval(parse(text = paste("normal.theta", names.31[i], sep = "."))))
-    }
-    normal.theta = do.call(rbind, ll)
-    return(normal.theta)
-}
-
-```

From 0597edfbe335c59462b36c2a7072da3b85876d68 Mon Sep 17 00:00:00 2001
From: StefanGam <154674303+StefanGam@users.noreply.github.com>
Date: Thu, 19 Dec 2024 23:40:18 +0200
Subject: [PATCH 45/63] Create README.md in folder

---
 MuPoMo_normalization/README.md | 22 ++++++++++++++++++++++
 1 file changed, 22 insertions(+)
 create mode 100644 MuPoMo_normalization/README.md

diff --git a/MuPoMo_normalization/README.md b/MuPoMo_normalization/README.md
new file mode 100644
index 0000000..e2a96da
--- /dev/null
+++ b/MuPoMo_normalization/README.md
@@ -0,0 +1,22 @@
+<div style="margin: 0; padding: 0; text-align: center; border: none;">
+<a href="https://quantlet.com" target="_blank" style="text-decoration: none; border: none;">
+<img src="https://github.com/StefanGam/test-repo/blob/main/quantlet_design.png?raw=true" alt="Header Image" width="100%" style="margin: 0; padding: 0; display: block; border: none;" />
+</a>
+</div>
+
+```
+Name of QuantLet: MuPoMo_normalization
+
+Published in: MuPoMo
+
+Description: 'Normalizes optimal shape variation parameters theta estimated from MuPoMo_optimization, and will be
+
+Keywords: 'time series, demography, mortality, population, normalization'
+
+See also: 'MuPoMo_data, MuPoMo_optimization, MuPoMo_referencecurve,
+
+Author: Lei Fang
+
+Submitted: Mon, June 13 2016 by Lei Fang
+
+```

From 22cad2dbb9ba05532d9d95d7cba922d572a6e38a Mon Sep 17 00:00:00 2001
From: StefanGam <154674303+StefanGam@users.noreply.github.com>
Date: Thu, 19 Dec 2024 23:40:20 +0200
Subject: [PATCH 46/63] Delete existing MuPoMo_optimization/README.md

---
 MuPoMo_optimization/README.md | 108 ----------------------------------
 1 file changed, 108 deletions(-)
 delete mode 100644 MuPoMo_optimization/README.md

diff --git a/MuPoMo_optimization/README.md b/MuPoMo_optimization/README.md
deleted file mode 100644
index bca74c7..0000000
--- a/MuPoMo_optimization/README.md
+++ /dev/null
@@ -1,108 +0,0 @@
-
-[<img src="https://github.com/QuantLet/Styleguide-and-FAQ/blob/master/pictures/banner.png" width="888" alt="Visit QuantNet">](http://quantlet.de/)
-
-## [<img src="https://github.com/QuantLet/Styleguide-and-FAQ/blob/master/pictures/qloqo.png" alt="Visit QuantNet">](http://quantlet.de/) **MuPoMo_optimization** [<img src="https://github.com/QuantLet/Styleguide-and-FAQ/blob/master/pictures/QN2.png" width="60" alt="Visit QuantNet 2.0">](http://quantlet.de/)
-
-```yaml
-
-Name of QuantLet : MuPoMo_optimization
-
-Published in : MuPoMo
-
-Description : 'Optimizes shape variation parameters theta based on kt and reference curve to update
-new kt, and will be called in MuPoMo_main_twopop and MuPoMo_main_multipop.'
-
-Keywords : 'time series, demography, mortality, population, nonlinear, optimization, non parametric
-smoothing'
-
-See also : 'MuPoMo_data, MuPoMo_normalization, MuPoMo_referencecurve, MuPoMo_main_twopop,
-MuPoMo_main_multipop, MuPoMo_bootstrap'
-
-Author : Lei Fang, Juhyun Park
-
-Submitted : Mon, June 13 2016 by Lei Fang
-
-```
-
-
-### R Code:
-```r
-optimization = function(theta, kt, kt.reference) {
-           t = time(kt)
- t.reference = time(kt.reference)
-    
-    ### loss function
-    loss = function(theta, t, kt, t.reference, kt.reference) {
-        ## assume theta[1]>0, theta[3]>0, if not, take absolute values
-        theta1 = abs(theta[1])
-        theta2 = theta[2]
-        theta3 = abs(theta[3])
-        
-        if (theta[1] < 0 | theta[3] < 0) 
-            warning("theta1 or theta3 <0, abs value is used")
-        sm.t = (t.reference - theta2)/theta3  # time adjustment
-        ## common domain for kt and time-adjusted kt.reference
-        tmin = max(min(t), min(sm.t))
-        tmax = min(max(t), max(sm.t))
-        i0   = which(t >= tmin & t <= tmax)  # index for common domain
-        if (length(i0) > 0) {
-            t0 = t[i0]
-            ## smooth interpolation of shifted kt.reference on common grid
-            dref = data.frame(sm.t = sm.t, kt.reference = kt.reference)
-            # sm: sm.regression with optimal smoothing parameter
-            h.optimal3 = h.select(sm.t, kt.reference)
-            sm = sm.regression(sm.t, kt.reference, h = h.optimal3, eval.points = t0, model = "none", poly.index = 1, display = "none")
-            mu = theta1 * sm$estimate
-            ## mean squared error at common grid points
-            mse = mean((kt[i0] - mu)^2)  # mse of kt and the modelled one
-        } else {
-            mse = 1e+09
-        }
-        return(mse)
-    }
-    
-    ### parameter estimation with nonlinear optimization
-    conv   = 1
-    theta0 = theta
-    while (conv != 0) {
-        # check convergence
-        out    = optim(theta0, loss, gr = NULL, t, kt, t.reference, kt.reference, control = list(maxit = 1000))  # optimization
-        conv   = out$convergence
-        theta0 = out$par
-    }
-    ### constraint on theta2 (time shift parameter)
-    if (out$par[2] >= -200 & out$par[2] <= 200) 
-        temp.par = out$par else temp.par = theta
-    result = c(temp.par, out$value, out$convergence)
-    
-    ### check results on graph
-    theta  = result[1:3]
-    theta1 = abs(theta[1])
-    theta2 = theta[2]
-    theta3 = abs(theta[3])
-    
-    sm.t   = (t.reference - theta2)/theta3  # time adjustment
-    ## common grid for kt and shifted kt.reference
-    tmin   = max(min(t), min(sm.t))
-    tmax   = min(max(t), max(sm.t))
-    i0     = which(t >= tmin & t <= tmax)
-    t0     = t[i0]
-    ## shifted curves (kt.hat)
-    dref   = data.frame(sm.t = sm.t, kt.reference = kt.reference)
-    
-    # sm: sm.regression with optimal smoothing parameter
-    h.optimal4 = h.select(sm.t, kt.reference)
-    sm         = sm.regression(sm.t, kt.reference, h = h.optimal4, eval.points = sm.t, model = "none", poly.index = 1, display = "none")
-    mu         = theta1 * sm$estimate
-    mu         = ts(mu, start = sm.t[1], frequency = theta3)
-    
-    # sm: sm.regression with optimal smoothing parameter
-    h.optimal5 = h.select(sm.t, kt.reference)
-    sm0        = sm.regression(sm.t, kt.reference, h = h.optimal5, eval.points = t0, model = "none", poly.index = 1, display = "none")
-    mu0        = theta1 * sm0$estimate
-    mu0        = ts(mu0, start = t0[1], frequency = 1)
-    
-    return(list(result, mu, mu0, tmin, tmax))
-}
-
-```

From 88ae85b5768840d04c29bc28cd4c18276bcc38b6 Mon Sep 17 00:00:00 2001
From: StefanGam <154674303+StefanGam@users.noreply.github.com>
Date: Thu, 19 Dec 2024 23:40:23 +0200
Subject: [PATCH 47/63] Create README.md in folder

---
 MuPoMo_optimization/README.md | 22 ++++++++++++++++++++++
 1 file changed, 22 insertions(+)
 create mode 100644 MuPoMo_optimization/README.md

diff --git a/MuPoMo_optimization/README.md b/MuPoMo_optimization/README.md
new file mode 100644
index 0000000..c1bbcd4
--- /dev/null
+++ b/MuPoMo_optimization/README.md
@@ -0,0 +1,22 @@
+<div style="margin: 0; padding: 0; text-align: center; border: none;">
+<a href="https://quantlet.com" target="_blank" style="text-decoration: none; border: none;">
+<img src="https://github.com/StefanGam/test-repo/blob/main/quantlet_design.png?raw=true" alt="Header Image" width="100%" style="margin: 0; padding: 0; display: block; border: none;" />
+</a>
+</div>
+
+```
+Name of QuantLet: MuPoMo_optimization
+
+Published in: MuPoMo
+
+Description: 'Optimizes shape variation parameters theta based on kt and reference curve
+
+Keywords: 'time series, demography, mortality, population, nonlinear, optimization, non parametric smoothing'
+
+See also: 'MuPoMo_data, MuPoMo_normalization, MuPoMo_referencecurve,
+
+Author: Lei Fang, Juhyun Park
+
+Submitted: Mon, June 13 2016 by Lei Fang
+
+```

From 95726d2be755095e6f81a8f5f5fac95245471d7f Mon Sep 17 00:00:00 2001
From: StefanGam <154674303+StefanGam@users.noreply.github.com>
Date: Thu, 19 Dec 2024 23:40:25 +0200
Subject: [PATCH 48/63] Delete existing MuPoMo_referencecurve/README.md

---
 MuPoMo_referencecurve/README.md | 51 ---------------------------------
 1 file changed, 51 deletions(-)
 delete mode 100644 MuPoMo_referencecurve/README.md

diff --git a/MuPoMo_referencecurve/README.md b/MuPoMo_referencecurve/README.md
deleted file mode 100644
index 9d30b61..0000000
--- a/MuPoMo_referencecurve/README.md
+++ /dev/null
@@ -1,51 +0,0 @@
-
-[<img src="https://github.com/QuantLet/Styleguide-and-FAQ/blob/master/pictures/banner.png" width="888" alt="Visit QuantNet">](http://quantlet.de/)
-
-## [<img src="https://github.com/QuantLet/Styleguide-and-FAQ/blob/master/pictures/qloqo.png" alt="Visit QuantNet">](http://quantlet.de/) **MuPoMo_referencecurve** [<img src="https://github.com/QuantLet/Styleguide-and-FAQ/blob/master/pictures/QN2.png" width="60" alt="Visit QuantNet 2.0">](http://quantlet.de/)
-
-```yaml
-
-Name of QuantLet : MuPoMo_referencecurve
-
-Published in : MuPoMo
-
-Description : 'Regenerates reference curve (common trend) based on normalized optimal theta
-parameters and smoothed original kt, and will be called in MuPoMo_main_multipop.'
-
-Keywords : time series, demography, mortality, population, normalization
-
-See also : 'MuPoMo_data, MuPoMo_optimization, MuPoMo_normalization, MuPoMo_main_twopop,
-MuPoMo_main_multipop, MuPoMo_bootstrap'
-
-Author : Lei Fang
-
-Submitted : Mon, June 13 2016 by Lei Fang
-
-```
-
-
-### R Code:
-```r
-referencecurve  = function(theta2, theta3, kt, kt.null) {
-    t           = time(kt)
-    sm.t        = theta3 * t + theta2  # time adjustment
-    t.reference = Sweden$year
-    ## common grid for kt and shifted kt.reference
-    tmin = max(min(t.reference), min(sm.t))
-    tmax = min(max(t.reference), max(sm.t))
-    i0   = which(t.reference >= tmin & t.reference <= tmax)
-    if (length(i0) > 0) {
-        t0  = t.reference[i0]
-        d   = data.frame(kt, sm.t)
-        # sm: sm.regression with optimal smoothing parameter
-        h.optimal6 = h.select(sm.t, kt)
-        sm  = sm.regression(sm.t, kt, h = h.optimal6, eval.points = t0, model = "none", poly.index = 1, display = "none")
-        mu1 = sm$estimate
-        mu  = ts(mu1, start = t0[1], frequency = 1)
-    } else {
-        mu  = kt.null
-    }
-    return(mu)
-}
-
-```

From 30bc6c7384259e56cb63190cd52e7ae23afedf3b Mon Sep 17 00:00:00 2001
From: StefanGam <154674303+StefanGam@users.noreply.github.com>
Date: Thu, 19 Dec 2024 23:40:27 +0200
Subject: [PATCH 49/63] Create README.md in folder

---
 MuPoMo_referencecurve/README.md | 22 ++++++++++++++++++++++
 1 file changed, 22 insertions(+)
 create mode 100644 MuPoMo_referencecurve/README.md

diff --git a/MuPoMo_referencecurve/README.md b/MuPoMo_referencecurve/README.md
new file mode 100644
index 0000000..3785b37
--- /dev/null
+++ b/MuPoMo_referencecurve/README.md
@@ -0,0 +1,22 @@
+<div style="margin: 0; padding: 0; text-align: center; border: none;">
+<a href="https://quantlet.com" target="_blank" style="text-decoration: none; border: none;">
+<img src="https://github.com/StefanGam/test-repo/blob/main/quantlet_design.png?raw=true" alt="Header Image" width="100%" style="margin: 0; padding: 0; display: block; border: none;" />
+</a>
+</div>
+
+```
+Name of QuantLet: MuPoMo_referencecurve
+
+Published in: MuPoMo
+
+Description: 'Regenerates reference curve (common trend) based on normalized optimal theta parameters and smoothed original kt,
+
+Keywords: 'time series, demography, mortality, population, normalization'
+
+See also: 'MuPoMo_data, MuPoMo_optimization, MuPoMo_normalization,
+
+Author: Lei Fang
+
+Submitted: Mon, June 13 2016 by Lei Fang
+
+```

From 9551e8b723aa905a1959cbedd63d30c5db27593b Mon Sep 17 00:00:00 2001
From: StefanGam <154674303+StefanGam@users.noreply.github.com>
Date: Sun, 26 Jan 2025 23:13:39 +0200
Subject: [PATCH 50/63] Delete existing MuPoMo_bootstrap/README.md

---
 MuPoMo_bootstrap/README.md | 32 --------------------------------
 1 file changed, 32 deletions(-)
 delete mode 100644 MuPoMo_bootstrap/README.md

diff --git a/MuPoMo_bootstrap/README.md b/MuPoMo_bootstrap/README.md
deleted file mode 100644
index 3cb3482..0000000
--- a/MuPoMo_bootstrap/README.md
+++ /dev/null
@@ -1,32 +0,0 @@
-<div style="margin: 0; padding: 0; text-align: center; border: none;">
-<a href="https://quantlet.com" target="_blank" style="text-decoration: none; border: none;">
-<img src="https://github.com/StefanGam/test-repo/blob/main/quantlet_design.png?raw=true" alt="Header Image" width="100%" style="margin: 0; padding: 0; display: block; border: none;" />
-</a>
-</div>
-
-```
-Name of QuantLet: MuPoMo_bootstrap
-
-Published in: MuPoMo
-
-Description: 'Forecasts mortality rates based on a semi-parametric approach, and bootstraps time series with innovation to compute the prediction intervals. Uses random two countries to demonstrate.'
-
-Keywords: 'time series, demography, mortality, population, nonparametric smoothing, parametric modelling, Lee-Carter method,
-
-See also: 'MuPoMo_data, MuPoMo_optimization, MuPoMo_normalization,
-
-Author: Lei Fang
-
-Submitted: Mon, June 13 2016 by Lei Fang
-
-Example: 
-
-```
-<div align="center">
-<img src="https://raw.githubusercontent.com/QuantLet/MuPoMo/master/MuPoMo_bootstrap/Histogram%20of%20theta1.png" alt="Image" />
-</div>
-
-<div align="center">
-<img src="https://raw.githubusercontent.com/QuantLet/MuPoMo/master/MuPoMo_bootstrap/Prediction%20intervals%20at%20different%20levels.png" alt="Image" />
-</div>
-

From 94b682e06c5d97db00386a3b0b7c84e1099e2638 Mon Sep 17 00:00:00 2001
From: StefanGam <154674303+StefanGam@users.noreply.github.com>
Date: Sun, 26 Jan 2025 23:13:41 +0200
Subject: [PATCH 51/63] Create README.md in folder

---
 MuPoMo_bootstrap/README.md | 34 ++++++++++++++++++++++++++++++++++
 1 file changed, 34 insertions(+)
 create mode 100644 MuPoMo_bootstrap/README.md

diff --git a/MuPoMo_bootstrap/README.md b/MuPoMo_bootstrap/README.md
new file mode 100644
index 0000000..fcf400a
--- /dev/null
+++ b/MuPoMo_bootstrap/README.md
@@ -0,0 +1,34 @@
+<div style="margin: 0; padding: 0; text-align: center; border: none;">
+<a href="https://quantlet.com" target="_blank" style="text-decoration: none; border: none;">
+<img src="https://github.com/StefanGam/test-repo/blob/main/quantlet_design.png?raw=true" alt="Header Image" width="100%" style="margin: 0; padding: 0; display: block; border: none;" />
+</a>
+</div>
+
+```
+Name of QuantLet: MuPoMo_bootstrap
+
+Published in: MuPoMo
+
+Description: Forecasts mortality rates based on a semi-parametric approach, and bootstraps time series with innovation to compute the prediction intervals. Uses random two countries to demonstrate.
+
+Keywords: time series, demography, mortality, population, nonparametric smoothing, parametric modelling, Lee-Carter method,
+
+See also: MuPoMo_data, MuPoMo_optimization, MuPoMo_normalization,
+
+Author: Lei Fang
+
+Submitted: Mon, June 13 2016 by Lei Fang
+
+Example: 
+- Prediction intervals at different levels
+- Histogram of theta1
+
+```
+<div align="center">
+<img src="https://raw.githubusercontent.com/QuantLet/MuPoMo/master/MuPoMo_bootstrap/Histogram%20of%20theta1.png" alt="Image" />
+</div>
+
+<div align="center">
+<img src="https://raw.githubusercontent.com/QuantLet/MuPoMo/master/MuPoMo_bootstrap/Prediction%20intervals%20at%20different%20levels.png" alt="Image" />
+</div>
+

From 4ba4314996eb9eda75e350c22bd36457aeb3f94b Mon Sep 17 00:00:00 2001
From: StefanGam <154674303+StefanGam@users.noreply.github.com>
Date: Sun, 26 Jan 2025 23:13:43 +0200
Subject: [PATCH 52/63] Delete existing MuPoMo_data/README.md

---
 MuPoMo_data/README.md | 22 ----------------------
 1 file changed, 22 deletions(-)
 delete mode 100644 MuPoMo_data/README.md

diff --git a/MuPoMo_data/README.md b/MuPoMo_data/README.md
deleted file mode 100644
index 69d07dc..0000000
--- a/MuPoMo_data/README.md
+++ /dev/null
@@ -1,22 +0,0 @@
-<div style="margin: 0; padding: 0; text-align: center; border: none;">
-<a href="https://quantlet.com" target="_blank" style="text-decoration: none; border: none;">
-<img src="https://github.com/StefanGam/test-repo/blob/main/quantlet_design.png?raw=true" alt="Header Image" width="100%" style="margin: 0; padding: 0; display: block; border: none;" />
-</a>
-</div>
-
-```
-Name of QuantLet: MuPoMo_data
-
-Published in: MuPoMo
-
-Description: 'Reads data from Human Mortality Database and calculate kt, and will be called
-
-Keywords: 'time series, demography, mortality, Lee-Carter method, population, Human Mortality Database'
-
-See also: 'MuPoMo_optimization, MuPoMo_normalization, MuPoMo_referencecurve,
-
-Author: Lei Fang
-
-Submitted: Mon, June 13 2016 by Lei Fang
-
-```

From 2c9bdb6f901b142993bb49f337997381b570002d Mon Sep 17 00:00:00 2001
From: StefanGam <154674303+StefanGam@users.noreply.github.com>
Date: Sun, 26 Jan 2025 23:13:45 +0200
Subject: [PATCH 53/63] Create README.md in folder

---
 MuPoMo_data/README.md | 22 ++++++++++++++++++++++
 1 file changed, 22 insertions(+)
 create mode 100644 MuPoMo_data/README.md

diff --git a/MuPoMo_data/README.md b/MuPoMo_data/README.md
new file mode 100644
index 0000000..625e515
--- /dev/null
+++ b/MuPoMo_data/README.md
@@ -0,0 +1,22 @@
+<div style="margin: 0; padding: 0; text-align: center; border: none;">
+<a href="https://quantlet.com" target="_blank" style="text-decoration: none; border: none;">
+<img src="https://github.com/StefanGam/test-repo/blob/main/quantlet_design.png?raw=true" alt="Header Image" width="100%" style="margin: 0; padding: 0; display: block; border: none;" />
+</a>
+</div>
+
+```
+Name of QuantLet: MuPoMo_data
+
+Published in: MuPoMo
+
+Description: Reads data from Human Mortality Database and calculate kt, and will be called
+
+Keywords: time series, demography, mortality, Lee-Carter method, population, Human Mortality Database
+
+See also: MuPoMo_optimization, MuPoMo_normalization, MuPoMo_referencecurve,
+
+Author: Lei Fang
+
+Submitted: Mon, June 13 2016 by Lei Fang
+
+```

From b149d1e303e7f0be97b9993bac25ecd7b768ccb2 Mon Sep 17 00:00:00 2001
From: StefanGam <154674303+StefanGam@users.noreply.github.com>
Date: Sun, 26 Jan 2025 23:13:46 +0200
Subject: [PATCH 54/63] Delete existing MuPoMo_main_multipop/README.md

---
 MuPoMo_main_multipop/README.md | 32 --------------------------------
 1 file changed, 32 deletions(-)
 delete mode 100644 MuPoMo_main_multipop/README.md

diff --git a/MuPoMo_main_multipop/README.md b/MuPoMo_main_multipop/README.md
deleted file mode 100644
index cab21b5..0000000
--- a/MuPoMo_main_multipop/README.md
+++ /dev/null
@@ -1,32 +0,0 @@
-<div style="margin: 0; padding: 0; text-align: center; border: none;">
-<a href="https://quantlet.com" target="_blank" style="text-decoration: none; border: none;">
-<img src="https://github.com/StefanGam/test-repo/blob/main/quantlet_design.png?raw=true" alt="Header Image" width="100%" style="margin: 0; padding: 0; display: block; border: none;" />
-</a>
-</div>
-
-```
-Name of QuantLet: MuPoMo_main_multipop
-
-Published in: MuPoMo
-
-Description: 'Estimates and forecasts mortality rates based on a semi-parametric approach, which applies parametric modelling for
-
-Keywords: 'time series, demography, mortality, population, nonparametric smoothing, parametric modelling, Lee-Carter method'
-
-See also: 'MuPoMo_data, MuPoMo_optimization, MuPoMo_normalization,
-
-Author: Lei Fang
-
-Submitted: Mon, June 13 2016 by Lei Fang
-
-Example: 
-
-```
-<div align="center">
-<img src="https://raw.githubusercontent.com/QuantLet/MuPoMo/master/MuPoMo_main_multipop/Multi-Population%20model%20with%20German%20data.png" alt="Image" />
-</div>
-
-<div align="center">
-<img src="https://raw.githubusercontent.com/QuantLet/MuPoMo/master/MuPoMo_main_multipop/Multi-Population%20model%20with%20Japanese%20data.png" alt="Image" />
-</div>
-

From ae68cc02308cf387a0b374959df759b59d122ff2 Mon Sep 17 00:00:00 2001
From: StefanGam <154674303+StefanGam@users.noreply.github.com>
Date: Sun, 26 Jan 2025 23:13:48 +0200
Subject: [PATCH 55/63] Create README.md in folder

---
 MuPoMo_main_multipop/README.md | 34 ++++++++++++++++++++++++++++++++++
 1 file changed, 34 insertions(+)
 create mode 100644 MuPoMo_main_multipop/README.md

diff --git a/MuPoMo_main_multipop/README.md b/MuPoMo_main_multipop/README.md
new file mode 100644
index 0000000..80bb453
--- /dev/null
+++ b/MuPoMo_main_multipop/README.md
@@ -0,0 +1,34 @@
+<div style="margin: 0; padding: 0; text-align: center; border: none;">
+<a href="https://quantlet.com" target="_blank" style="text-decoration: none; border: none;">
+<img src="https://github.com/StefanGam/test-repo/blob/main/quantlet_design.png?raw=true" alt="Header Image" width="100%" style="margin: 0; padding: 0; display: block; border: none;" />
+</a>
+</div>
+
+```
+Name of QuantLet: MuPoMo_main_multipop
+
+Published in: MuPoMo
+
+Description: Estimates and forecasts mortality rates based on a semi-parametric approach, which applies parametric modelling for
+
+Keywords: time series, demography, mortality, population, nonparametric smoothing, parametric modelling, Lee-Carter method
+
+See also: MuPoMo_data, MuPoMo_optimization, MuPoMo_normalization,
+
+Author: Lei Fang
+
+Submitted: Mon, June 13 2016 by Lei Fang
+
+Example: 
+- Multi-Population model with German data
+- Multi-Population model with Japanese data
+
+```
+<div align="center">
+<img src="https://raw.githubusercontent.com/QuantLet/MuPoMo/master/MuPoMo_main_multipop/Multi-Population%20model%20with%20German%20data.png" alt="Image" />
+</div>
+
+<div align="center">
+<img src="https://raw.githubusercontent.com/QuantLet/MuPoMo/master/MuPoMo_main_multipop/Multi-Population%20model%20with%20Japanese%20data.png" alt="Image" />
+</div>
+

From 74b7dd7532c7558f70c2b074839328e2ec0e09a6 Mon Sep 17 00:00:00 2001
From: StefanGam <154674303+StefanGam@users.noreply.github.com>
Date: Sun, 26 Jan 2025 23:13:50 +0200
Subject: [PATCH 56/63] Delete existing MuPoMo_main_twopop/README.md

---
 MuPoMo_main_twopop/README.md | 44 ------------------------------------
 1 file changed, 44 deletions(-)
 delete mode 100644 MuPoMo_main_twopop/README.md

diff --git a/MuPoMo_main_twopop/README.md b/MuPoMo_main_twopop/README.md
deleted file mode 100644
index 4f6e122..0000000
--- a/MuPoMo_main_twopop/README.md
+++ /dev/null
@@ -1,44 +0,0 @@
-<div style="margin: 0; padding: 0; text-align: center; border: none;">
-<a href="https://quantlet.com" target="_blank" style="text-decoration: none; border: none;">
-<img src="https://github.com/StefanGam/test-repo/blob/main/quantlet_design.png?raw=true" alt="Header Image" width="100%" style="margin: 0; padding: 0; display: block; border: none;" />
-</a>
-</div>
-
-```
-Name of QuantLet: MuPoMo_main_twopop
-
-Published in: MuPoMo
-
-Description: 'Estimates and forecasts mortality rates based on a semi-parametric approach, which applies parametric modelling for
-
-Keywords: 'time series, demography, mortality, population, nonparametric smoothing, parametric modelling, Lee-Carter method,
-
-See also: 'MuPoMo_data, MuPoMo_optimization, MuPoMo_normalization,
-
-Author: Lei Fang
-
-Submitted: Mon, June 13 2016 by Lei Fang
-
-Example: 
-
-```
-<div align="center">
-<img src="https://raw.githubusercontent.com/QuantLet/MuPoMo/master/MuPoMo_main_twopop/Contour%20plot%20of%20theta2%20and%20theta4.png" alt="Image" />
-</div>
-
-<div align="center">
-<img src="https://raw.githubusercontent.com/QuantLet/MuPoMo/master/MuPoMo_main_twopop/Loss%20function%20of%20theta2.png" alt="Image" />
-</div>
-
-<div align="center">
-<img src="https://raw.githubusercontent.com/QuantLet/MuPoMo/master/MuPoMo_main_twopop/Loss%20surface%203D.png" alt="Image" />
-</div>
-
-<div align="center">
-<img src="https://raw.githubusercontent.com/QuantLet/MuPoMo/master/MuPoMo_main_twopop/Model%20fit%20and%20forecast.png" alt="Image" />
-</div>
-
-<div align="center">
-<img src="https://raw.githubusercontent.com/QuantLet/MuPoMo/master/MuPoMo_main_twopop/Time%20shift%20at%20different%20levels.png" alt="Image" />
-</div>
-

From c3c410c20c244b0499ae6c9af718b33767ed8364 Mon Sep 17 00:00:00 2001
From: StefanGam <154674303+StefanGam@users.noreply.github.com>
Date: Sun, 26 Jan 2025 23:13:52 +0200
Subject: [PATCH 57/63] Create README.md in folder

---
 MuPoMo_main_twopop/README.md | 49 ++++++++++++++++++++++++++++++++++++
 1 file changed, 49 insertions(+)
 create mode 100644 MuPoMo_main_twopop/README.md

diff --git a/MuPoMo_main_twopop/README.md b/MuPoMo_main_twopop/README.md
new file mode 100644
index 0000000..2ace6bf
--- /dev/null
+++ b/MuPoMo_main_twopop/README.md
@@ -0,0 +1,49 @@
+<div style="margin: 0; padding: 0; text-align: center; border: none;">
+<a href="https://quantlet.com" target="_blank" style="text-decoration: none; border: none;">
+<img src="https://github.com/StefanGam/test-repo/blob/main/quantlet_design.png?raw=true" alt="Header Image" width="100%" style="margin: 0; padding: 0; display: block; border: none;" />
+</a>
+</div>
+
+```
+Name of QuantLet: MuPoMo_main_twopop
+
+Published in: MuPoMo
+
+Description: Estimates and forecasts mortality rates based on a semi-parametric approach, which applies parametric modelling for
+
+Keywords: time series, demography, mortality, population, nonparametric smoothing, parametric modelling, Lee-Carter method,
+
+See also: MuPoMo_data, MuPoMo_optimization, MuPoMo_normalization,
+
+Author: Lei Fang
+
+Submitted: Mon, June 13 2016 by Lei Fang
+
+Example: 
+- Time shift at different levels
+- Loss function of theta2
+- Loss surface 3D
+- Contour plot of theta2 and theta4
+- Model fit and forecast
+
+```
+<div align="center">
+<img src="https://raw.githubusercontent.com/QuantLet/MuPoMo/master/MuPoMo_main_twopop/Contour%20plot%20of%20theta2%20and%20theta4.png" alt="Image" />
+</div>
+
+<div align="center">
+<img src="https://raw.githubusercontent.com/QuantLet/MuPoMo/master/MuPoMo_main_twopop/Loss%20function%20of%20theta2.png" alt="Image" />
+</div>
+
+<div align="center">
+<img src="https://raw.githubusercontent.com/QuantLet/MuPoMo/master/MuPoMo_main_twopop/Loss%20surface%203D.png" alt="Image" />
+</div>
+
+<div align="center">
+<img src="https://raw.githubusercontent.com/QuantLet/MuPoMo/master/MuPoMo_main_twopop/Model%20fit%20and%20forecast.png" alt="Image" />
+</div>
+
+<div align="center">
+<img src="https://raw.githubusercontent.com/QuantLet/MuPoMo/master/MuPoMo_main_twopop/Time%20shift%20at%20different%20levels.png" alt="Image" />
+</div>
+

From 940d8782df0af5bdb57150d66354b399d45acf90 Mon Sep 17 00:00:00 2001
From: StefanGam <154674303+StefanGam@users.noreply.github.com>
Date: Sun, 26 Jan 2025 23:13:53 +0200
Subject: [PATCH 58/63] Delete existing MuPoMo_normalization/README.md

---
 MuPoMo_normalization/README.md | 22 ----------------------
 1 file changed, 22 deletions(-)
 delete mode 100644 MuPoMo_normalization/README.md

diff --git a/MuPoMo_normalization/README.md b/MuPoMo_normalization/README.md
deleted file mode 100644
index e2a96da..0000000
--- a/MuPoMo_normalization/README.md
+++ /dev/null
@@ -1,22 +0,0 @@
-<div style="margin: 0; padding: 0; text-align: center; border: none;">
-<a href="https://quantlet.com" target="_blank" style="text-decoration: none; border: none;">
-<img src="https://github.com/StefanGam/test-repo/blob/main/quantlet_design.png?raw=true" alt="Header Image" width="100%" style="margin: 0; padding: 0; display: block; border: none;" />
-</a>
-</div>
-
-```
-Name of QuantLet: MuPoMo_normalization
-
-Published in: MuPoMo
-
-Description: 'Normalizes optimal shape variation parameters theta estimated from MuPoMo_optimization, and will be
-
-Keywords: 'time series, demography, mortality, population, normalization'
-
-See also: 'MuPoMo_data, MuPoMo_optimization, MuPoMo_referencecurve,
-
-Author: Lei Fang
-
-Submitted: Mon, June 13 2016 by Lei Fang
-
-```

From 8a281c78458f7848614ed97100dac073cbaec77e Mon Sep 17 00:00:00 2001
From: StefanGam <154674303+StefanGam@users.noreply.github.com>
Date: Sun, 26 Jan 2025 23:13:55 +0200
Subject: [PATCH 59/63] Create README.md in folder

---
 MuPoMo_normalization/README.md | 22 ++++++++++++++++++++++
 1 file changed, 22 insertions(+)
 create mode 100644 MuPoMo_normalization/README.md

diff --git a/MuPoMo_normalization/README.md b/MuPoMo_normalization/README.md
new file mode 100644
index 0000000..2517f17
--- /dev/null
+++ b/MuPoMo_normalization/README.md
@@ -0,0 +1,22 @@
+<div style="margin: 0; padding: 0; text-align: center; border: none;">
+<a href="https://quantlet.com" target="_blank" style="text-decoration: none; border: none;">
+<img src="https://github.com/StefanGam/test-repo/blob/main/quantlet_design.png?raw=true" alt="Header Image" width="100%" style="margin: 0; padding: 0; display: block; border: none;" />
+</a>
+</div>
+
+```
+Name of QuantLet: MuPoMo_normalization
+
+Published in: MuPoMo
+
+Description: Normalizes optimal shape variation parameters theta estimated from MuPoMo_optimization, and will be
+
+Keywords: time series, demography, mortality, population, normalization
+
+See also: MuPoMo_data, MuPoMo_optimization, MuPoMo_referencecurve,
+
+Author: Lei Fang
+
+Submitted: Mon, June 13 2016 by Lei Fang
+
+```

From 00e0aa35f122ef34f3e7ff4b5420c48db941d3da Mon Sep 17 00:00:00 2001
From: StefanGam <154674303+StefanGam@users.noreply.github.com>
Date: Sun, 26 Jan 2025 23:13:57 +0200
Subject: [PATCH 60/63] Delete existing MuPoMo_optimization/README.md

---
 MuPoMo_optimization/README.md | 22 ----------------------
 1 file changed, 22 deletions(-)
 delete mode 100644 MuPoMo_optimization/README.md

diff --git a/MuPoMo_optimization/README.md b/MuPoMo_optimization/README.md
deleted file mode 100644
index c1bbcd4..0000000
--- a/MuPoMo_optimization/README.md
+++ /dev/null
@@ -1,22 +0,0 @@
-<div style="margin: 0; padding: 0; text-align: center; border: none;">
-<a href="https://quantlet.com" target="_blank" style="text-decoration: none; border: none;">
-<img src="https://github.com/StefanGam/test-repo/blob/main/quantlet_design.png?raw=true" alt="Header Image" width="100%" style="margin: 0; padding: 0; display: block; border: none;" />
-</a>
-</div>
-
-```
-Name of QuantLet: MuPoMo_optimization
-
-Published in: MuPoMo
-
-Description: 'Optimizes shape variation parameters theta based on kt and reference curve
-
-Keywords: 'time series, demography, mortality, population, nonlinear, optimization, non parametric smoothing'
-
-See also: 'MuPoMo_data, MuPoMo_normalization, MuPoMo_referencecurve,
-
-Author: Lei Fang, Juhyun Park
-
-Submitted: Mon, June 13 2016 by Lei Fang
-
-```

From 4e47b39ded3c1d818bff2e47641d786bf08dd580 Mon Sep 17 00:00:00 2001
From: StefanGam <154674303+StefanGam@users.noreply.github.com>
Date: Sun, 26 Jan 2025 23:13:59 +0200
Subject: [PATCH 61/63] Create README.md in folder

---
 MuPoMo_optimization/README.md | 22 ++++++++++++++++++++++
 1 file changed, 22 insertions(+)
 create mode 100644 MuPoMo_optimization/README.md

diff --git a/MuPoMo_optimization/README.md b/MuPoMo_optimization/README.md
new file mode 100644
index 0000000..c8e1105
--- /dev/null
+++ b/MuPoMo_optimization/README.md
@@ -0,0 +1,22 @@
+<div style="margin: 0; padding: 0; text-align: center; border: none;">
+<a href="https://quantlet.com" target="_blank" style="text-decoration: none; border: none;">
+<img src="https://github.com/StefanGam/test-repo/blob/main/quantlet_design.png?raw=true" alt="Header Image" width="100%" style="margin: 0; padding: 0; display: block; border: none;" />
+</a>
+</div>
+
+```
+Name of QuantLet: MuPoMo_optimization
+
+Published in: MuPoMo
+
+Description: Optimizes shape variation parameters theta based on kt and reference curve
+
+Keywords: time series, demography, mortality, population, nonlinear, optimization, non parametric smoothing
+
+See also: MuPoMo_data, MuPoMo_normalization, MuPoMo_referencecurve,
+
+Author: Lei Fang, Juhyun Park
+
+Submitted: Mon, June 13 2016 by Lei Fang
+
+```

From ed49228d37aa446a8509eb69993e0e37363c3973 Mon Sep 17 00:00:00 2001
From: StefanGam <154674303+StefanGam@users.noreply.github.com>
Date: Sun, 26 Jan 2025 23:14:01 +0200
Subject: [PATCH 62/63] Delete existing MuPoMo_referencecurve/README.md

---
 MuPoMo_referencecurve/README.md | 22 ----------------------
 1 file changed, 22 deletions(-)
 delete mode 100644 MuPoMo_referencecurve/README.md

diff --git a/MuPoMo_referencecurve/README.md b/MuPoMo_referencecurve/README.md
deleted file mode 100644
index 3785b37..0000000
--- a/MuPoMo_referencecurve/README.md
+++ /dev/null
@@ -1,22 +0,0 @@
-<div style="margin: 0; padding: 0; text-align: center; border: none;">
-<a href="https://quantlet.com" target="_blank" style="text-decoration: none; border: none;">
-<img src="https://github.com/StefanGam/test-repo/blob/main/quantlet_design.png?raw=true" alt="Header Image" width="100%" style="margin: 0; padding: 0; display: block; border: none;" />
-</a>
-</div>
-
-```
-Name of QuantLet: MuPoMo_referencecurve
-
-Published in: MuPoMo
-
-Description: 'Regenerates reference curve (common trend) based on normalized optimal theta parameters and smoothed original kt,
-
-Keywords: 'time series, demography, mortality, population, normalization'
-
-See also: 'MuPoMo_data, MuPoMo_optimization, MuPoMo_normalization,
-
-Author: Lei Fang
-
-Submitted: Mon, June 13 2016 by Lei Fang
-
-```

From d20917785c87b26de0461f71c955aec04c88c0fa Mon Sep 17 00:00:00 2001
From: StefanGam <154674303+StefanGam@users.noreply.github.com>
Date: Sun, 26 Jan 2025 23:14:03 +0200
Subject: [PATCH 63/63] Create README.md in folder

---
 MuPoMo_referencecurve/README.md | 22 ++++++++++++++++++++++
 1 file changed, 22 insertions(+)
 create mode 100644 MuPoMo_referencecurve/README.md

diff --git a/MuPoMo_referencecurve/README.md b/MuPoMo_referencecurve/README.md
new file mode 100644
index 0000000..2665e22
--- /dev/null
+++ b/MuPoMo_referencecurve/README.md
@@ -0,0 +1,22 @@
+<div style="margin: 0; padding: 0; text-align: center; border: none;">
+<a href="https://quantlet.com" target="_blank" style="text-decoration: none; border: none;">
+<img src="https://github.com/StefanGam/test-repo/blob/main/quantlet_design.png?raw=true" alt="Header Image" width="100%" style="margin: 0; padding: 0; display: block; border: none;" />
+</a>
+</div>
+
+```
+Name of QuantLet: MuPoMo_referencecurve
+
+Published in: MuPoMo
+
+Description: Regenerates reference curve (common trend) based on normalized optimal theta parameters and smoothed original kt,
+
+Keywords: time series, demography, mortality, population, normalization
+
+See also: MuPoMo_data, MuPoMo_optimization, MuPoMo_normalization,
+
+Author: Lei Fang
+
+Submitted: Mon, June 13 2016 by Lei Fang
+
+```