Error distribution in GARCH models

[d952]

Hi, I have a question regarding to the chosing error distribution for ARCH/GARCH type models.
As I know, if a time series has fat tail, then it is not normally distributed and students t error distribution is more appropriate for that, but in my data when I estimate the volatility with students t I will have serial correlation even with including autoregressive term and trying different models, but when I run the model with normal error distribution then results are much more better in order to removing serial correlation. My question is that does it make sence to use normal distribution for a data big fat tail?

I appreciate if you reply me, many tahnks

[trubador]

GARCH is a flexible model and therefore there is no way to detect errors (if any) without seeing other diagnostics. You should either share the workfile along with your specifications or provide more output.

[d952]

GARCH is a flexible model and therefore there is no way to detect errors (if any) without seeing other diagnostics. You should either share the workfile along with your specifications or provide more output.

Thank you very much for your reply. Here I attach my workfile, I am estimating volatility for 12 metals (returns), I put the results for two metals in the workfile with students t and normal distribution, the rest of metals also have more or less the same results (expect two of them). As my data size is very big (alsmost 5000 observation) is it possible that makes the problem?

[trubador]

First of all, the mean equation is not stationary. You can add exogenous variables or use autoregressive lags to ensure the stationarity. If GARCH(1,1) model is still not able to capture the serial correlation, then it might call for a use of higher order model. This is usually the sign of time varying long-run volatility. And if that is indeed the case, then you might be able to successfully estimate a Component GARCH(1,1) model. You can also use variance regressors or try multivariate GARCH specifications to account for such strong residual serial correlation.

[d952]

First of all, the mean equation is not stationary. You can add exogenous variables or use autoregressive lags to ensure the stationarity. If GARCH(1,1) model is still not able to capture the serial correlation, then it might call for a use of higher order model. This is usually the sign of time varying long-run volatility. And if that is indeed the case, then you might be able to successfully estimate a Component GARCH(1,1) model. You can also use variance regressors or try multivariate GARCH specifications to account for such strong residual serial correlation.

Thank you very much for your reply. How did you recognize that the mean equation is not stationary? because constant is not significant?

[d952]

First of all, the mean equation is not stationary. You can add exogenous variables or use autoregressive lags to ensure the stationarity. If GARCH(1,1) model is still not able to capture the serial correlation, then it might call for a use of higher order model. This is usually the sign of time varying long-run volatility. And if that is indeed the case, then you might be able to successfully estimate a Component GARCH(1,1) model. You can also use variance regressors or try multivariate GARCH specifications to account for such strong residual serial correlation.

Thank you very much for your reply. How did you recognize that the mean equation is not stationary? because constant is not significant?

I just recognized that in the Ljung-BOX result for serial correlation within GARCH models is written that: "Probabilities may not be valid for this equation specification". It means that I cant rely on probabilities of Q-stat to recognize existance of serial correlation for GARCH models. Can you please tell me what is the reason? and apart from the visual detection is there any other solution for that?

[trubador]

The reason is that the degrees-of-freedom of chi-square changes in the case of ARMA models. In GARCH models, however, asymptotics may not hold and statistics should be corrected accordingly. While EViews does the necessary adjustment for ARMA models, it does not for the latter.

You can retrieve the standardized residuals after the estimation and then apply whatever method you need to obtain more robust Q statistics.