GARCH Calendar effects serial correlation

[Simon2803]

Hi All,

I have some issues with models for my undergraduate thesis and my supervisor is not particularly helpful. I am investigating calendar effects (month, day of the week, and trading month). What I have issues with is serial correlation. I am using greek, spanish and italian index returns. The variance significantly increases during the crisis. I am using EGARCH (1,1) - my supervisor told me to stick to 1,1 and GED error distribution not to impose any specific distribution. However when I regress the return on the individual dummies (i.e. return = c february march april ... december) for some of the data (for example spain) I get serial correlation when I check corellogram Q statistic. In one paper I saw that they included lagged dependent variable to correct for serial correlation, meaning after "december" dummy, comes "return(-1)" in the mean equation. I noticed that when I do this or even include 12 lags for monthly seasonality, or 5 lags for day seasonality or just include the ones that are significant (after estimating the regression with 12 lagged dependent variables - return(-2) return(-3)) my results are free of serial correlation, and they are stronger and more sensible than before (I do get January effect or monday effect). However I'm not sure if this method is correct, whether it is good to include the lagged dependent terms.

Please any advice would be welcomed. Thanks a lot!!

Simon

[trubador]

Yes, that is correct. You need to make sure that mean equation is stationary before moving on to model the variance part: http://forums.eviews.com/viewtopic.php? ... 635#p33814

[magister]

Yes, that is correct. You need to make sure that mean equation is stationary before moving on to model the variance part: http://forums.eviews.com/viewtopic.php? ... 635#p33814

I've got the same problem. I saw in some papers that they use FPEC (Final Prediction Error Criterion) as in Hsiao (1981) in order to determine the number of lags to be included into the equation. But this is quite difficult to apply, especially having a large sample.
I'm studying the day of the week effects. It is correct to apply the technique described by Simon in my case as well? Or could I just add the first lag of the dependent variable and assume that the serial correlation is eliminated and test for further correlation, after the GARCH models being applied? Or a MA(1) term?

Thank you.

[trubador]

There is no quick fix for that. This is not a problem per se, but is simply a part of the modeling process. You should run different models with alternate specifications and then compare the estimation results based on usual diagnostics. There is no way to know in advance the potential impact of AR(1) or MA(1) term on the GARCH estimation.

[magister]

There is no quick fix for that. This is not a problem per se, but is simply a part of the modeling process. You should run different models with alternate specifications and then compare the estimation results based on usual diagnostics. There is no way to know in advance the potential impact of AR(1) or MA(1) term on the GARCH estimation.

Yes, I do agree with you, but if you don't specify the model correctly from the very beginning, the results will be inconsistent and maybe having no statistic relevance whatsoever.
Anyway, it is methodologically correct to firstly include a lag of the dependent variable, run the GARCH model and further test for serial correlation? If found, to include the second lag, and re-run the model and so forth after the serial correlation is removed? Or to include in the mean equation the number of lags that are statistically significant, after testing for serial correlation?

Thank you.

LATER EDIT: In my regression, I'm using seasonal dummies, as independent variables, and mean return of stock market index, as dependent variable. I've modeled a VAR, with index return as endogenous variable and dummies as exogenous, with lag intervals set up by default. After, at the lag length criteria I've chosen the default value, FPE as the criterion in selecting lag. I've included these lags into my equation, run the GARCH model and I see that the model is free from serial correlation.

[trubador]

No one can specify the model correctly from the very beginning. That's why there are lots of diagnostic tools made available. This is really not a fragile field. You can and should try both approaches and see if you end up with the same model specification. If you don't, then you'll have a very nice finding to discuss.