# Variables importance on regression with ARIMA errors model

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:

1. Importance of external regressor
2. Importance of ARIMA coefs
3. 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?

1. $ARIMA(p,d,q)(P,D,Q)$ without external regressor
2. $ARIMA(0,0,0)(P,D,Q)$ with external regressor
3. $ARIMA(p,d,q)(0,0,0)$ with external regressor
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I realize this is a little late, but how are you selecting the ARIMA parameters? Obviously, if, for example, $(p,d,q)$ in model 1 is different from $(p,d,q)$ in the original model there will be some confounding of the effect of the external regressor with the change in $(p,d,q)$. –  jbowman Jun 10 '12 at 17:45