SARIMAX Model

A SARIMAX model is a time series model that combines seasonal autoregressive integrated moving average terms with exogenous regressors to model and forecast a single series.

SARIMAX 모형은 계절성 자기회귀누적이동평균 항과 외생 회귀변수를 결합하여 단일 시계열을 모형화하고 예측하는 시계열 모형이다.

How do I forecast a seasonal time series while including outside predictors?

외부 예측변수를 포함하여 계절성이 있는 시계열을 어떻게 예측하나요?

A SARIMAX model forecasts a time series using its own past values, past errors and seasonal patterns, plus external regressors such as promotions or holidays. It fits regularly spaced series with seasonality once the series has been made stationary through differencing.

When to use SARIMAX Model

• A regularly spaced series with trend and seasonal patterns
• Known external drivers such as prices, holidays or weather
• Forecasting with interpretable ARIMA terms and prediction intervals

When to use something else

• Several interacting series; use a vector autoregression
• Multiple seasonalities and irregular holidays with minimal tuning; use Prophet

Assumptions and requirements

• Stationarity after differencing
• Uncorrelated, constant-variance residuals
• Future values of exogenous regressors available for forecasting
• Regular time intervals

What the analysis reports

• Model orders (p,d,q)(P,D,Q)s
• Coefficients for AR, MA and exogenous terms
• AIC and BIC
• Ljung-Box test of residuals
• Forecasts with prediction intervals

How to report it

A SARIMAX([p],[d],[q])([P],[D],[Q])[s] model was selected by AIC, and Ljung-Box tests showed no residual autocorrelation, Q([df]) = [value], p = [value].

Related methods

• ARIMA Model
• Prophet Forecasting Model
• Exponential Smoothing

Run SARIMAX Model on Quorant