In a seasonal ARIMA model, ARIMA(p, d, q)(sp, sd, sq) m:
- p, d, and q are as in the nonseasonal model
- sp, sd, and sq are the seasonal analogs of p, d, and q
- m is the number of data points in each season
To calculate the coefficients of the input parameters, the Arima function uses this formula:
(1 - φ 1 B - … - φ p B p )(1 - Φ1 B m - … - Φ m*sp )(1 - B) d (1 - B m ) sd y t =
c + (1 + θ 1 B + … + θ q B q )(1 + Θ1 B m + … + Θ q B m*sq )e t
The Φ values are seasonal autoregressive parameters and the Θ values are seasonal moving average parameters.
The values B and e t are as defined as in the nonseasonal model.