One way to calculate importance of a variable in a regression, is to get the decrease in $RSS$ when we calculate a model without the variable in question.
Is this valid for a regression with ARIMA errors?
Suppose I want to get three measures:
- Importance of external regressor
- Importance of ARIMA coefs
- Importance of Seasonal ARIMA coefs
Would the decrease in $RSS$ if I compare the original $RSS$ with the $RSS$ the following models represent the measures I list above?
- $ARIMA(p,d,q)(P,D,Q)$ without external regressor
- $ARIMA(0,0,0)(P,D,Q)$ with external regressor
- $ARIMA(p,d,q)(0,0,0)$ with external regressor