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A-sa-overview.qmd
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# Seasonal Adjustment (SA) Overview {#sa-overview .unnumbered}
## In this chapter
This chapter is a first of a series focusing on the practical step by step use of JDemetra+ Seasonal Adjustment (SA) algorithms, restricted to monthly and quarterly series. For infra-monthly data see the [following chapter](#a-sa-hf). In the sections below an overview of the seasonal adjustment process is provided. The most widely used SA algorithms (Tramo-Seats and X13-Arima) have two steps: a pre-treatment to remove (temporarily) deterministic effects and a decomposition phase to estimate the seasonal factors.
The following chapters get into the specifics of each algorithm.
- [Pre-treatment](#sa-pre-t)
- [SA: X11 decomposition](a-sa-X11)
- [SA: Seats-decomposition](#a-sa-seats)
- [SA: Revision policies](#a-rev-pol)
- [SA of High-Frequency Data](#a-sa-hf)
- [SA: STL+ and MSTL+](#a-sa-stl)
- [X12+ and MX12+](a-sa-x12)
- [STS and MSTS](#a-sa-bsm)
The use of [graphical user interface](T-graphical-user-interface.qmd) and [R packages](T-r-packages.qmd) is described simultaneously whenever relevant.
In-depth methodological explanations of the algorithms are covered in separated chapters, in the [Methods](P_Methods.qmd) part of this book.
More information on the steps and best practices of a seasonal adjustment process can be found in the [Eurostat guidelines on seasonal adjustment](https://ec.europa.eu/eurostat/documents/3859598/6830795/KS-GQ-15-001-EN-N.pdf)
For an overview on the algorithms and methodological issues, the user can refer to the [Handbook on Seasonal Adjustment](https://ec.europa.eu/eurostat/documents/3859598/8939616/KS-GQ-18-001-EN-N.pdf)
## SA process
The goal of seasonal adjustment is to remove seasonal fluctuations from a time series. Seasonal fluctuations are quasi-periodic infra-annual movements. They can mask evolutions of greater interest for the user such as short term evolution or long time trends.
When setting up the process:
- seasonality tests (can also be done in the frame of quality assessment at the end)
- trading days correction set up if relevant
- [regressors generation](#a-cal)
- regressors selection
- estimation with selected algorithm (see section below), might be [automated with the cruncher](#t-prod)
- [quality report](#t-prod)
- selective editing and manual fine tuning of parameters, re-estimation if needed
- updating when new data available with tailored [revision policy](#a-rev-pol)
<!-- ## Quick Start -->
<!-- (chap à part?) -->
<!-- To launch a -->
<!-- en mode cahier d'exos -->
<!-- #a-sa-X11-q-start -->
<!-- #a-sa-seats-q-start -->
## Seasonal Adjustment Algorithms
<!-- Extensions for high frequency data tackled in frequency part -->
Two categories of algorithms :
- historical core (main): X-13-Arima and Tramo-Seats [improved in version 3](#v3-vs-v2-sa)
- version 3 additional algorithms (incubator)
X13-ARIMA and TRAMO-SEATS are two-step algorithms with a pre-treatment phase (Reg-Arima or Tramo) and a decomposition phase (X11 and Seats).
STL+ combines STL local regression based decomposition and a simplified Reg-Arima pre-treatment restricted to airline models.
X12+ combines X11 (enhanced) decomposition and a simplified Reg-Arima pre-treatment restricted to airline models.
Seats+ combines Seats decomposition and a simplified Reg-Arima pre-treatment restricted to airline models.
In a [Structural Time Series](#a-sa-bsm) approach pre-treatment and decomposition are done simultaneously in a State Space Framework.
## Admissible data frequencies
For low frequency data
- in version 3.x $p$ in ${2,3,4,6,12}$ is admissible in all algorithms
- in version 3.x $p$ in ${2,3,4,6,12}$ is admissible in Tramo-Seats and $p$ in ${2,4,12}$ is admissible in X-13.
Algorithms extended for high-frequency (infra-monthly) data can be applied to "any periodicity" in their R version and to $p$ in ${7, 52.18, 365.25}$ in the graphical user interface, see [here](#a-sa-hf) for more details.
## Decomposition in unobserved components
To seasonally adjust a series, seasonal factors $S_{t}$ will be estimated and removed from the original raw series: $Y_{sa}=Y_{t}/S_{t}$ or $Y_{sa}=Y_{t}-S_{t}$. To do so the series is first decomposed into unobservable components. Two decomposition models [^a-sa-overview-1] are used in JDemetra+ :
[^a-sa-overview-1]: other options as the log-additive model are also available in a more specific context described [here](#a-sa-X11-settings)
- The additive model: $X_{t} = T_{t} + S_{t} + I_{t}$;
- The multiplicative model: $X_{t} = T_{t} \times S_{t} \times I_{t}$.
The main components, each representing the impact of certain types of phenomena on the time series ($X_{t}$), are:
- The trend ($T_{t}$) that captures long-term and medium-term behaviour;
- The seasonal component ($S_{t}$) representing intra-year fluctuations, monthly or quarterly, that are repeated more or less regularly year after year;
- The irregular component ($I_{t}$) combining all the other more or less erratic fluctuations not covered by the previous components.
In general, the trend consists of 2 sub-components:
- The long-term evolution of the series;
- The cycle, that represents the smooth, almost periodic movement around the long-term evolution of the series. It reveals a succession of phases of growth and recession. Trend and cycle are not separated in SA algorithms.
## Detecting seasonal patterns
A large number of [seasonality tests](#m-tests) are available in JDemetra+. They can be accessed in the graphical user interface or via R.
### In R
In rjd3toolkit package:
- Canova-Hansen (`seasonality.canovahansen()`)
- X-12 combined test (`seasonality.combined()`)
- F-test on seasonal dummies (`seasonality.f()`)
- Friedman Seasonality Test (`seasonality.friedman()`)
- Kruskall-Wallis Seasonality Test (`seasonality.kruskalwallis()`)
- Periodogram Seasonality Test (`seasonality.periodogram()`)
- QS Seasonality Test (`seasonality.qs()`)
Full documentation of those functions can be found [here](https://rjdverse.github.io/rjd3toolkit/reference/index.html)
### In GUI
How to perform tests in the graphical user interface is described [here](#t-GUI-tstools-tests).
## Direct or Indirect seasonal adjustment
when seasonally adjusting series which are aggregates following a given classification, the user has to chose whether directly adjust the aggregate from its raw version or to aggregate the adjusted components.
The graphical user interface in version 2.x provides a [module](#direct-indirect) to compare the two options. It won't be provided in version 3.x.