I have a very basic question on including constant in Arima models. I'll illustrate this by an example. I have the following ACF and PACF of a weekly time series that is differenced at lag 1 (trend) and lag 52 (seasonality). The series becomes stationary after differencing. In looking at the ACF and PACF I see that the appropriate model is an MA(1) model or a simple exponential smoothing (SES), so I end up with (0,1,1)X(0,1,0)x52.
- When I include a constant I get a linear trend aka. Arima with drift or SES with drift.
- When I do not include a constant, I get a flat forecast which is reasonable for the series at hand.
How can I objectively determine, if we need to include a constant term or not ?