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Hi,

I have applied EGARCH model with Student's t error distributions on intraday returns of FOREX market. when I used simple garch model I got reasonable outcomes but the P-values are very high. but when I applied the egarch and I drop one of the dummies which is the dummy for monday 9:00 AM suddenly I got all coefficients positive (which is strange for returns on financial data) and all p-values are 0.0000 !!! but the interesting point is we I plot them on a graph both models show the same shape while the egarch one is above the simple garch and all positive. Last thing is results are almost same when I drop the constant or when I drop one dummy which is OK I think.

I have attached a snap shot of the outcomes.

Any suggestion?

Cheers,
Siroos

It is difficult to tell solely based on this output. Other diagnostics are needed for a more thorough analysis. Having said that, simple GARCH estimation results indicate that the stationarity condition (a+b<1) is not fulfilled, and the coefficient of GARCH is relatively weak. Small p-values are expected, since you have a very large sample. Try turning off "Backcast presample MA terms" in such complex models to see if it improves the results. You can also try alternative GARCH-M specifications.

Thank you very much trubador for the interesting points. I will apply these but running the model takes some time.

I have checked the stationarity of the returns again and ADF and PP unit root tests give p-value around 0.0001 which we can conclude that returns are stationary. Turning off the "Backcast presample MA terms" also wouldn't give any improvement same as different GARCH-M specifications. The only issue remains is dropping the dummy variables in order to avoid perfect multicollinearity. I am trying different approaches such as instead of dropping 9:00 am maybe we can drop 13:00 or 16:30 or maybe it is better to drop whole wednesday.

Any suggestions would be grately appreciated!!!

Cheers,
Siroos

It is "very" difficult to make suggestions without seeing the actual data in your case. All I can say is that empirical characteristics of intraday data is quite different from that of other lower frequencies (i.e. daily) and therefore, regular GARCH-type methods might not work well or cannot be directly applied (without preliminary analysis) at such high frequencies. You may not be able to make your data stationary or your data may simply display long memory or have significant structural breaks. Whatever is your case, usual diagnostic tests may not be much of a help.