Seasonal dummies in a sarima and a time series model with sarima errors

[newsagent]

Does it make sense to include seasonal dummies

1. in a sarima model
2. in a regression model with sarima errors

[robjhyndman]

These are the same model, and is equivalent to using all available Fourier terms in a dynamic harmonic regression.

Usually you would not include seasonal terms in both the ARIMA part of the model and the regression part of the model, because it makes interpretation more difficult, and both are trying to capture the same information. But it is possible, and then the seasonal part of the ARIMA model would be modelling deviations from fixed seasonality.