SARIMA(1,0,1)(1,0,1,12)

SARIMA (Seasonal Autoregressive Integrated Moving Average) is a type of time series model that includes both autoregressive and moving average components, as well as seasonal factors.

The notation SARIMA(p,d,q)(P,D,Q,s) represents the parameters of the model.

In this case, SARIMA(1,0,1)(1,0,1,12) means:

- p = 1: The autoregressive order is 1, meaning that the model includes the previous value in the time series as a predictor.
- d = 0: There is no differencing applied to the time series.
- q = 1: The moving average order is 1, meaning that the model includes the previous error term in the prediction.
- P = 1: The seasonal autoregressive order is 1, meaning that the model includes the previous season's value as a predictor.
- D = 0: There is no seasonal differencing applied to the time series.
- Q = 1: The seasonal moving average order is 1, meaning that the model includes the previous season's error term in the prediction.
- s = 12: The time series has a seasonal period of 12 (monthly data), meaning that the model takes into account the seasonal changes over a period of 12 months.

In summary, this SARIMA model uses the previous value and previous error term as predictors, as well as the previous season's value and error term. It does not include any differencing, but takes into account the seasonal changes over a period of 12 months.