I have data on GDP, employment rate, inflation and production on two countries and I like to make some ARIMA models. I have done this before, but not with including regressors. Also, the time period includes the European crisis, so I created a dummy for this period. I know that I can select the best ARIMA model by checking the AIC and BIC values. But I have to play around with the regressors, maybe it is better not to include them all. Also, I have to check if the dummy is necessary to include or not (Chow test). How do I start?
- First, I select the appropriate ARIMA model (using AIC and BIC), using all regressors, but not the dummy.
- Then, when looking at the significance of the regressors, select the one to use and which not (how to do?).
- Then compare this model with the same model including the dummy and perform a Chow test on whether to include it or not.
But I feel like there are many more combinations of regressors and the dummy and so on, like I did not test all possible models. What is the right approach?