SARIMAX — Seasonal ARIMA with Exogenous Regressors
Also known as: seasonal ARIMA with exogenous variables, SARIMA with regressors, ARIMAX, SARIMAX — Dışsal Değişkenli Mevsimsel ARIMA
SARIMAX extends the seasonal ARIMA (Box-Jenkins) model by adding exogenous explanatory variables, so it can capture the effect of holidays, economic indicators, or policy variables on a time series. It combines non-seasonal and seasonal autoregressive and moving-average dynamics with external regressors, and is estimated by maximum likelihood in state-space form.
Key highlights
- Captures the effect of external drivers — holidays, economic indicators, policy variables — on top of the series' own seasonal and autoregressive dynamics.
- Handles both seasonal and non-seasonal dependence within one unified, well-established Box-Jenkins framework.
- Estimated by maximum likelihood in state-space form, giving coherent forecasts and interpretable regression coefficients for the exogenous terms.
Intuition
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How it works
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When to use it
Use SARIMAX for a single continuous time series that shows seasonality and is also driven by known external variables you can supply for the forecast horizon. It needs a reasonably long history (at least about 48 observations to identify seasonal structure). The key assumptions are that the series can be made stationary through differencing, that the exogenous regressors are known in advance for the periods you want to forecast, and that the model residuals are free of autocorrelation. It is less suitable when the future values of the external drivers are unknown, when the series is too short to pin down the seasonal pattern, or when relationships are strongly non-linear.
Strengths & limitations
- Captures the effect of external drivers — holidays, economic indicators, policy variables — on top of the series' own seasonal and autoregressive dynamics.
- Handles both seasonal and non-seasonal dependence within one unified, well-established Box-Jenkins framework.
- Estimated by maximum likelihood in state-space form, giving coherent forecasts and interpretable regression coefficients for the exogenous terms.
- Requires the future values of the exogenous regressors to be known over the forecast horizon, which is often not the case.
- Needs a fairly long series (roughly 48+ observations) to identify the seasonal structure reliably.
- The series must be made stationary by differencing, and residuals must be checked for autocorrelation; violations undermine the forecasts.
Common pitfalls
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Applications
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Frequently asked
How is SARIMAX different from plain SARIMA?
SARIMA models a series only from its own past and seasonal pattern. SARIMAX adds exogenous regressors (the X term), so it can also account for the effect of known external variables such as holidays, economic indicators, or policy changes.
Why do I need future values of the exogenous variables?
Because the model attributes part of the series' movement to those external drivers, it cannot forecast forward without knowing their future values. You must supply the exogenous regressors over the whole forecast horizon, which is why they should be quantities that are known or independently forecastable in advance.
How long does my series need to be?
Roughly 48 observations or more, so the seasonal structure can be identified reliably. Shorter series make the seasonal AR and MA terms hard to estimate.
What should I check after fitting?
Confirm the differenced series is stationary and that the residuals show no remaining autocorrelation. Autocorrelated residuals mean the model has missed structure and the forecasts and intervals will be unreliable.
Sources
- 1.Hyndman, R. J. & Athanasopoulos, G. (2021). Forecasting: Principles and Practice (3rd ed.). OTexts.
- 2.Box, G. E. P., Jenkins, G. M., Reinsel, G. C. & Ljung, G. M. (2015). Time Series Analysis: Forecasting and Control (5th ed.). Wiley.ISBN 978-1118675021
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Cite this page
ScholarGate. (2026, June 1). SARIMAX. ScholarGate. https://scholargate.app/econometrics/sarimax