I have a question concerning the significance of the seasonal dummies in my ARIMA-model (I do not use seasonal differencing or seasonal AR/MA as I have quite regular seasonality and I get better performance results):
What to do, if say 1 or 2 are significant but the rest are not? This happens to me particularly when I use monthly dummies. Shall I exclude the insignificant dummy variables?
If I do so (say I exclude from 11 monthly dummies the dummies for February, March), this will lead to a change again in the significance and coefficients of the remaining monthly dummy variables significantly!
I could not find any information on that in my standard forecasting textbooks.
Finally I found a reference which I wanted to share to conclude the post:
The exclusion of some seasonal dummies because their estimated coefficients have low t-scores is not recommended. Preferably, testing seasonal dummy coefficients should be done with the F-Test instead of with the t-test because seasonality is usually a single compound hypothesis rather than 3 (or 11 with monthly data) individual hypothesis having to do with each quarter (or month). To the extent that a hypothesis is a joint one, it should be tested with the F-Test. If the hypothesis of seasonal variation can be summarized into a single dummy variable, then the use of the t-test will cause no problems. Often, where seasonal dummies are unambiguously called for, no hypothesis testing at all is undertaking.
Studenmund, A.H. and Cassidy, H.J. (1997). Using econometrics: A practical guide. The Addison-Wesley series in economics, 3rd ed., p. 257, Addison-Wesley, Reading, Mass.