diff --git a/Time-Series-Crash-Course/17. ARIMA.ipynb b/Time-Series-Crash-Course/17. ARIMA.ipynb index b8141a8..0afa3e1 100644 --- a/Time-Series-Crash-Course/17. ARIMA.ipynb +++ b/Time-Series-Crash-Course/17. ARIMA.ipynb @@ -1,4342 +1 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "id": "44de62a1", - "metadata": {}, - "source": [ - "# How To Forecast Time-Series Using Autoregression\n" - ] - }, - { - "cell_type": "markdown", - "id": "53fd97cc", - "metadata": {}, - "source": [ - "## Intro\n" - ] - }, - { - "cell_type": "markdown", - "id": "7a1f2981", - "metadata": {}, - "source": [ - "In my previous posts we have covered autoregession (AR) and moving-average (MA) models. However, do you know what is better than these two models? A single model that combines them!\n", - "\n", - "Autoregressive Integrated Moving Average better known as ARIMA, is probably the most used time series forecasting model and is combination of the individual aforementioned models.\n", - "\n", - "In this article, I want to dive into the theory and framework behind the ARIMA model. Then, we will go through a simple Python walkthrough in carrying out forecast with ARIMA using the statsmodels package!\n" - ] - }, - { - "cell_type": "markdown", - "id": "1c88cde9", - "metadata": {}, - "source": [ - "## What Is Moving Average Mode?\n", - "\n" - ] - }, - { - "cell_type": "markdown", - "id": "d241068b", - "metadata": {}, - "source": [ - "### Overview" - ] - }, - { - "cell_type": "markdown", - "id": "e0fd3550", - "metadata": {}, - "source": [ - "As stated above, ARIMA stands for AutoRegressive Integrated Moving Average is basically just a combination of the three (in reality two) components:\n" - ] - }, - { - "cell_type": "markdown", - "id": "5b8780c6", - "metadata": {}, - "source": [ - "**AutoRegressive (AR):**" - ] - }, - { - "cell_type": "markdown", - "id": "32a7f737", - "metadata": {}, - "source": [ - "This is just autoregression, where we forecast future values using a linear combination of the previously observed values:" - ] - }, - { - "attachments": { - "Screenshot%202023-10-22%20at%2012.45.07.png": { - "image/png": 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" - } - }, - "cell_type": "markdown", - "id": "8e1166be", - "metadata": {}, - "source": [ - "![Screenshot%202023-10-22%20at%2012.45.07.png](attachment:Screenshot%202023-10-22%20at%2012.45.07.png)" - ] - }, - { - "cell_type": "markdown", - "id": "a9698a7b", - "metadata": {}, - "source": [ - "Here y is the time series we are forecasting at multiple time steps, ϕ are the coefficients of the lags, ε is the error term (often normally distributed) and p is the number of lagged components, also known as the order." - ] - }, - { - "cell_type": "markdown", - "id": "176c2858", - "metadata": {}, - "source": [ - "**Integrated (I):**" - ] - }, - { - "cell_type": "markdown", - "id": "8425d23d", - "metadata": {}, - "source": [ - "The middle part of the ARIMA model is named integrated. This is the number (order d) of differencing required to make the time series stationary.\n", - "\n", - "Stationarity is where the time series has a constant mean and variance, meaning the statistical properties of the series does not change through time. Differencing de-trends a time series and tends to make the mean constant. You can apply differencing several times, but often the series is sufficiently stationary after a single differencing step.\n", - "\n", - "It is important to note, that this integrated part only makes the mean constant. We need to apply another transform such as the logarithmic and Box-Cox transform to generate a constant variance (more on this later)." - ] - }, - { - "cell_type": "markdown", - "id": "e2206a52", - "metadata": {}, - "source": [ - "**Moving Average (MA):**" - ] - }, - { - "cell_type": "markdown", - "id": "36a4c4b4", - "metadata": {}, - "source": [ - "The last component is the moving average where you forecast using past forecast errors instead of the actual observed values:" - ] - }, - { - "attachments": { - "Screenshot%202023-10-22%20at%2015.02.08.png": { - "image/png": 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" - } - }, - "cell_type": "markdown", - "id": "8e3c7be6", - "metadata": {}, - "source": [ - "![Screenshot%202023-10-22%20at%2015.02.08.png](attachment:Screenshot%202023-10-22%20at%2015.02.08.png)" - ] - }, - { - "cell_type": "markdown", - "id": "6c1de170", - "metadata": {}, - "source": [ - "Here y is the time series we are forecasting at multiple time steps, μ is the mean, θ are the coefficients of the lagged forecast errors, ε are the forecast error terms and q is the number of lagged error components.\n" - ] - }, - { - "cell_type": "markdown", - "id": "ba1edb97", - "metadata": {}, - "source": [ - "**Final Form:**" - ] - }, - { - "cell_type": "markdown", - "id": "ac7b0f4c", - "metadata": {}, - "source": [ - "Combining all these components together, we can write the full model as:\n" - ] - }, - { - "attachments": { - "Screenshot%202023-10-22%20at%2015.13.58.png": { - "image/png": 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- } - }, - "cell_type": "markdown", - "id": "a02b842c", - "metadata": {}, - "source": [ - "![Screenshot%202023-10-22%20at%2015.13.58.png](attachment:Screenshot%202023-10-22%20at%2015.13.58.png)" - ] - }, - { - "cell_type": "markdown", - "id": "2022b600", - "metadata": {}, - "source": [ - "Where y’ refers to the differenced version of the time series.\n", - "\n", - "This is the full ARIMA equation and is just a linear summation of the three components. The model is usefully written in a short-hand way as ARIMA(p, d, q) where p, d and q refer to the order of autoregressors, differencing and moving-averages components respectively." - ] - }, - { - "cell_type": "markdown", - "id": "c83ae609", - "metadata": {}, - "source": [ - "### Requirements" - ] - }, - { - "cell_type": "markdown", - "id": "aec96ee1", - "metadata": {}, - "source": [ - "As we touched upon earlier, the differencing component is there to help make the time series stationary. This is because the ARIMA model requires the data to be stationary for it to adequately model it. The mean is stabilised through differencing and the variance can be stabilised through the Box-Cox transform as we mentioned above.\n" - ] - }, - { - "cell_type": "markdown", - "id": "590a7ba8", - "metadata": {}, - "source": [ - "### Order Selection" - ] - }, - { - "cell_type": "markdown", - "id": "8a136902", - "metadata": {}, - "source": [ - "One of the preprocessing steps is to determine the optimal orders (p, d, q) of our ARIMA model. The simplest one is the order of differencing d as this can be verified by carrying out a statistical test for stationarity. The most popular one is the Augmented Dickey-Fuller (ADF), where the null hypothesis is that the time series is not stationary.\n", - "\n", - "The autoregressive and moving-average orders (p,q) can be deduced by analysing the partial autocorrelation function (PACF) and autocorrelation function respectively. The gist of of this method is to plot a correlogram of the various lags/forecast errors of the time series to determine which are statistically significant. If this seems arbitrary at the moment don’t worry, in the Python tutorial later we will walkthrough this process.\n", - "\n", - "However, a more thorough technique is to simply iterate over all the possible combinations of orders and choose the model with the best score against a metric such as Akaike’s Information Criterion (AIC) or Bayesian Information Criterion (BIC). This is analogous to regular hyperparameter tuning and definitely the more robust method, but is more computational expensive of course.\n" - ] - }, - { - "cell_type": "markdown", - "id": "07207f6a", - "metadata": {}, - "source": [ - "### Estimation" - ] - }, - { - "cell_type": "markdown", - "id": "ba76f754", - "metadata": {}, - "source": [ - "After choosing our orders, we then need to find their optimal corresponding coefficients. This where the need for stationarity comes in. As declared above, a stationary time series has constant statistical properties such as mean and variance. Therefore, all the data points are part of the same probability distribution, which makes fitting our model easier. Furthermore, forecasts are treated as random variables and will now belong to the same probability distribution as the newly generated stationary time series. Overall, it helps make the data in the future be somewhat like the past.\n", - "\n", - "As the stationary data belongs to some distribution (frequently the normal distribution), we can estimate the coefficients using Maximum Likelihood Estimation (MLE). MLE deduces the optimal values of the coefficients that produce the highest probability of obtaining that data. The MLE for normally distributed data, is the same result as carrying ordinary least squares. Therefore, least squares is also frequently used for this exact reason." - ] - }, - { - "cell_type": "markdown", - "id": "a683b945", - "metadata": {}, - "source": [ - "## Python Walkthrough\n", - "\n" - ] - }, - { - "cell_type": "markdown", - "id": "8f9dfeb7", - "metadata": {}, - "source": [ - "### Data" - ] - }, - { - "cell_type": "code", - "execution_count": 1, - "id": "6fcce2e2", - "metadata": {}, - "outputs": [ - { - "data": { - "text/html": [ - " \n", - " " - ] - }, - "metadata": {}, - "output_type": "display_data" - }, - { - "data": { - "application/vnd.plotly.v1+json": { - "config": { - "plotlyServerURL": "https://plot.ly" - }, - "data": [ - { - "hovertemplate": "Date=%{x}
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" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "# Import packages \n", - "from scipy.stats import boxcox\n", - "\n", - "# Make the target variance stationary\n", - "data['Passengers_Boxcox'], lam = boxcox(data['#Passengers'])\n", - "\n", - "# Plot the box-cox passenger data\n", - "plot_passenger_volumes(df=data, y='Passengers_Boxcox')" - ] - }, - { - "cell_type": "markdown", - "id": "df04a10e", - "metadata": {}, - "source": [ - "The data now appears to be stationary. We could have made it further stationary by carrying out second order differencing or seasonal differencing, however I think it is satisfactory here." - ] - }, - { - "cell_type": "markdown", - "id": "2d37fa49", - "metadata": {}, - "source": [ - "### Modelling" - ] - }, - { - "cell_type": "markdown", - "id": "9af48e94", - "metadata": {}, - "source": [ - "In the previous sections, I mentioned how you can find the autoregressive and moving-average orders by plotting the autocorrelation and partial autocorrelation functions. Let’s show an example of how you can do it here:" - ] - }, - { - "cell_type": "code", - "execution_count": 4, - "id": "af5fac80", - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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\n", 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\n", 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" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "# Import packages\n", - "import matplotlib.pyplot as plt\n", - "from statsmodels.graphics.tsaplots import plot_pacf, plot_acf\n", - "\n", - "# Difference the data\n", - "data[\"Passenger_diff\"] = data[\"Passengers_Boxcox\"].diff()\n", - "data.dropna(inplace=True)\n", - "\n", - "# Plot acf and pacf\n", - "fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(16,5), dpi=80)\n", - "plot_acf(data['Passenger_diff'])\n", - "plot_pacf(data['Passenger_diff'], method='ywm')\n", - "ax1.tick_params(axis='both', labelsize=12)\n", - "ax2.tick_params(axis='both', labelsize=12)\n", - "plt.show()" - ] - }, - { - "cell_type": "markdown", - "id": "59d21b4a", - "metadata": {}, - "source": [ - "The blue region signifies where the points are no longer statistically significant and from the plot we see the last lag that is statistically significant for both plot is ~12th. Therefore, we would take the order of p and q to be 12.\n", - "\n", - "Now, let’s fit the model using the ARIMA function and generate the forecasts:" - ] - }, - { - "cell_type": "code", - "execution_count": 5, - "id": "b67566ad", - "metadata": {}, - "outputs": [ - { - "name": "stderr", - "output_type": "stream", - "text": [ - "/Users/egorhowell/opt/anaconda3/lib/python3.9/site-packages/statsmodels/tsa/base/tsa_model.py:471: ValueWarning:\n", - "\n", - "An unsupported index was provided and will be ignored when e.g. forecasting.\n", - "\n", - "/Users/egorhowell/opt/anaconda3/lib/python3.9/site-packages/statsmodels/tsa/base/tsa_model.py:471: ValueWarning:\n", - "\n", - "An unsupported index was provided and will be ignored when e.g. forecasting.\n", - "\n", - "/Users/egorhowell/opt/anaconda3/lib/python3.9/site-packages/statsmodels/tsa/base/tsa_model.py:471: ValueWarning:\n", - "\n", - "An unsupported index was provided and will be ignored when e.g. forecasting.\n", - "\n", - "/Users/egorhowell/opt/anaconda3/lib/python3.9/site-packages/statsmodels/tsa/statespace/sarimax.py:966: UserWarning:\n", - "\n", - "Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.\n", - "\n", - "/Users/egorhowell/opt/anaconda3/lib/python3.9/site-packages/statsmodels/tsa/statespace/sarimax.py:978: UserWarning:\n", - "\n", - "Non-invertible starting MA parameters found. Using zeros as starting parameters.\n", - "\n", - "/Users/egorhowell/opt/anaconda3/lib/python3.9/site-packages/statsmodels/base/model.py:604: ConvergenceWarning:\n", - "\n", - "Maximum Likelihood optimization failed to converge. Check mle_retvals\n", - "\n", - "/Users/egorhowell/opt/anaconda3/lib/python3.9/site-packages/statsmodels/tsa/base/tsa_model.py:834: ValueWarning:\n", - "\n", - "No supported index is available. Prediction results will be given with an integer index beginning at `start`.\n", - "\n" - ] - } - ], - "source": [ - "# Import packages\n", - "from statsmodels.tsa.arima.model import ARIMA\n", - "from scipy.special import inv_boxcox\n", - "\n", - "# Split train and test\n", - "train = data.iloc[:-int(len(data) * 0.2)]\n", - "test = data.iloc[-int(len(data) * 0.2):]\n", - "\n", - "# Build ARIMA model and inverse the boxcox\n", - "model = ARIMA(train['Passengers_Boxcox'], order=(12, 1, 12)).fit()\n", - "boxcox_forecasts = model.forecast(len(test))\n", - "forecasts = inv_boxcox(boxcox_forecasts, lam)" - ] - }, - { - "cell_type": "markdown", - "id": "c1f3f109", - "metadata": {}, - "source": [ - "### Results" - ] - }, - { - "cell_type": "markdown", - "id": "2051d9df", - "metadata": {}, - "source": [ - "The forecasts produced from this fitted model is for the differenced and Box-Cox transformed time series that we produced earlier. Therefore, we have to un-difference and apply the inverse Box-Cox transform to the predictions to acquire the actual airline passenger forecasted volumes:" - ] - }, - { - "cell_type": "code", - "execution_count": 6, - "id": "3bdaa5e8", - "metadata": {}, - "outputs": [ - { - "data": { - "application/vnd.plotly.v1+json": { - "config": { - "plotlyServerURL": "https://plot.ly" - }, - "data": [ - { - "name": "Train", - "type": "scatter", - "x": [ - "1949-03-01T00:00:00", - "1949-04-01T00:00:00", - "1949-05-01T00:00:00", - "1949-06-01T00:00:00", - "1949-07-01T00:00:00", - "1949-08-01T00:00:00", - "1949-09-01T00:00:00", - "1949-10-01T00:00:00", - "1949-11-01T00:00:00", - "1949-12-01T00:00:00", - "1950-01-01T00:00:00", - "1950-02-01T00:00:00", - "1950-03-01T00:00:00", - "1950-04-01T00:00:00", - "1950-05-01T00:00:00", - "1950-06-01T00:00:00", - "1950-07-01T00:00:00", - "1950-08-01T00:00:00", - "1950-09-01T00:00:00", - "1950-10-01T00:00:00", - "1950-11-01T00:00:00", - "1950-12-01T00:00:00", - "1951-01-01T00:00:00", - 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" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "# Import packages\n", - "import plotly.graph_objects as go\n", - "\n", - "def plot_forecasts(forecasts: list[float], title: str) -> None:\n", - " \"\"\"Function to plot the forecasts.\"\"\"\n", - " fig = go.Figure()\n", - " fig.add_trace(go.Scatter(x=train['Month'], y=train['#Passengers'], name='Train'))\n", - " fig.add_trace(go.Scatter(x=test['Month'], y=test['#Passengers'], name='Test'))\n", - " fig.add_trace(go.Scatter(x=test['Month'], y=forecasts, name='Forecast'))\n", - " fig.update_layout(template=\"simple_white\", font=dict(size=18), title_text=title,\n", - " width=650, title_x=0.5, height=400, xaxis_title='Date',\n", - " yaxis_title='Passenger Volume')\n", - "\n", - " return fig.show()\n", - "\n", - "\n", - "# Plot the forecasts\n", - "plot_forecasts(forecasts, 'ARIMA')" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "9356c1b6", - "metadata": {}, - "outputs": [], - "source": [] - } - ], - "metadata": { - "kernelspec": { - "display_name": "Python 3 (ipykernel)", - "language": "python", - "name": "python3" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.9.12" - } - }, - "nbformat": 4, - "nbformat_minor": 5 -} +arima