# When testing a hypothesis, should I keep an insignificant lag in ARMA-GARCH model?

I am trying to estimate ARMA-GARCH model for my stock returns time series.

I have estimated ARMA model for my series, and found that there exists ARCH, so added GARCH(1,1) term. However I now find previously significant ARMA coefficients being insignificant.

In this case, should I remove the insignificant ARMA terms? I am reluctant in doing so as I read from a book that it is not wise to remove ARMA terms judging from their significance.

Also, as I am not performing any predictions with this model (only using it as a normal return model for event study), I thought it would be unnecessary to do so?

• Could you give some more detail in how you are going to use the model? Feb 21 '17 at 7:49
• I specify my base model usimg arma-garch, then add date dummies to check for significance. If dummies are significant, that means there is an abnormal return. And no abnormal returns when dummies are insignificant Feb 21 '17 at 10:31
• What do you think about my answer? Mar 8 '17 at 19:40
• Please beware that statistical significance is not a black or white problem. The addition of extra terms increases estimation errors which themselves reduce significance. So I wouldn't worry too much if a 0.03 p-value suddenly becomes a 0.07 (I will assume 5% thresholds, but this applies to any significance level) This phenomenon is normal and there is nothing "magical" about 5%. I would be concerned, though, if a $10^{-8}$ p-value suddenly became a $0.38$, though. Which of these is your case? Jun 28 '19 at 8:38