ARIMA Model
- Order Selection of ARIMA Model
- ARIMA Modelling Procedure
(1) Plot the data and identify any unusual observations.
(2) If necessary, transform the data (using a Box-Cox Transformation) to stabilise the variance.
(3) If the data are non-stationary, take first differences of the data until the data are stationary.
(4) Examine the ACF/PACF: Is an ARIMA( p, d, 0 ) or ARIMA( 0, d, q ) model appropriate?
(5) Try your chosen model(s), and use the AICc to search for a better model.
(6) Check the residuals from your chosen model by plotting the ACF of the residuals, and doing a portmanteau test of the residuals. If they do not look like white noise, try a modified model.
(7) Once the residuals look like white noise, calculate forecasts.
Example: Seasonally adjusted electrical equipment orders
SARIMAX Model
- How to use SARIMA in Python ?
There are the following three steps to use SARIMAX model via Statsmodels library:
(i) Define the model.
(ii) Fit the defined model.
(iii) Make a prediction with the fit model.
from statsmodels.tsa.statespace.sarimax import SARIMAX
# Define model
'''
endog : observed time-series variable
exog : exogenous variables
order : (p, d, q)
seasonal_order : (P, D, Q, S)
trend : this parameter for controlling the deterministic trend polynomial A(t) as one of 'n','c','t','ct' for no trend, constant, linear, and constant with linear trend, respectively.
'''
model = SARIMAX( endog, exog, order, seasonal_order, trend, ... )
# Fit model
model_fit = model.fit()
# One step forecast
yhat = model_fit.predict( start, end )[1] Forecasting: Principles and Practice (2nd ed online version)( 簡體中文版 ), Rob J Hyndman and George Athanasopoulos
[2] statsmodels v0.13.0.dev0
[3] statsmodels.tsa.statespace.sarimax.SARIMAX
[1] Summary of rules for identifying ARIMA models, Robert Nau.
[2] ARIMA Model – Complete Guide to Time Series Forecasting in Python, Selva Prabhakaran, Aug 22, 2021.
[3] A Gentle Introduction to SARIMA for Time Series Forecasting in Python, Jason Brownlee, Aug 18, 2018.
[4] How to Grid Search SARIMA Hyperparameters for Time Series Forecasting, Jason Brownlee, Oct 24, 2018.
[5] Inflation Forecasting, Swati Sethee, Jun 8, 2020.
[6] Complete Guide To SARIMAX in Python for Time Series Modeling, Yugesh Verma, Jul 30, 2021.
[7] End-to-End Time Series Analysis and Forecasting: a Trio of SARIMAX, LSTM and Prophet (Part 1), Bruce Nguyen, Feb 7, 2021.