SARIMA Seasonal ARIMA
SARIMA adds seasonal structure to ARIMA so it can handle repeating cycles like weekly or yearly patterns.
The extra seasonal orders
SARIMA keeps the nonseasonal orders p, d, and q and adds a seasonal block written with capital P, D, and Q plus a period m.
- m is the season length, such as twelve for monthly data with a yearly cycle.
- Capital P is the seasonal autoregressive order, using values from prior seasons.
- Capital D is the seasonal differencing order, subtracting the value one season ago.
- Capital Q is the seasonal moving average order, using errors from prior seasons.
How it works
The seasonal terms operate at multiples of the period. For monthly data, a seasonal autoregressive term links this month to the same month last year. Seasonal differencing removes a stable yearly cycle just as ordinary differencing removes a trend.
Practical notes
- You must set the period m from domain knowledge or the ACF.
- More orders mean more parameters and a greater risk of overfitting.
- Automated search tools can scan order combinations for the best score.
Key idea
SARIMA layers seasonal autoregression, differencing, and moving average terms onto ARIMA to capture cycles at a known period.