0

I am trying to model gold and oil volatility but I am getting quite confusing results. I am using the rugarch package and using the standard GARCH and EGARCH to model volatility.

My results seems to indicate that the standard GARCH model with normal innovations is the best but I am reluctant to believe that as descriptive statistics indeed indicate that the returns are not normally distributed. What I find confusing also is that when using t-distribution instead of normal distribution the p-value for my correlation test decreases.

I was expecting to see the EGARCH outperform by a large margin but this doesn't seem to be the case. Hopefully someone will be able to clear that up for me. Here is a summary of my results.Summary

Can someone explain to me why I'm getting such inconclusive results?

ankc
  • 959
  • I am not familiar with the rugarch package, but are you interpreting this correctly? Based on the log-likelihood (presumably not the negative LL) your t innovations are doing better. What are the estimates of the degrees of freedom parameter? – tchakravarty Dec 09 '13 at 13:11
  • @fg nu,yes the log likelihood is better but the standardised squared residuals does not pass the ljung box test nor the arch lm test which is a necessity for a good model."What are the estimates of the degrees of freedom parameter?" I don't know what this is. – ankc Dec 09 '13 at 16:22
  • For the case of Gold returns compare the ARMA(0, 0)-EGARCH(1, 1) and ARMA(0, 0)-GARCH(1, 1) for t- and Normal distribution. Both are telling you that you have unmodeled GARCH effects, and that you need more lags in your GARCH specification. Other than those effects, the t distribution provides a better fit as discussed above. This seems pretty conclusive to me. – tchakravarty Dec 09 '13 at 16:47
  • Also, the t-distribution is characterized by a degrees of freedom parameter that tells you its scale. That is often useful in understanding the deviation from the normal distribution (t($\infty$) = N(0, 1)). – tchakravarty Dec 09 '13 at 16:50
  • @fg nu,The ARMA(0, 0)-GARCH(1, 1) for normal distribution seems fine to me, p-values are >0.05. Why is the p-value decreasing when I use the t-distribution?I agree the likelihood for t-distribution is higher but there is no point in that if the residuals doesn't pass the correlation test and I already tried higher order GARCH but the p-values doesn't seem to increase. – ankc Dec 09 '13 at 16:59
  • @fg nu, can you try replying to the above question?Thanks – ankc Dec 09 '13 at 18:31
  • To my knowledge there are two common cases where the ARCH LM test overrejects - 1. In the case that there is misspecification in the mean equation (Lumsdaine and Ng, JoE, 1999), and 2. In the case that there are additive outliers in the return series. It has been a while since I read this, but it might be able to explain some of your results. – tchakravarty Dec 09 '13 at 18:44
  • @fg nu,I tried different kinds of mean equation but got similar results, well I do think that there are quite a few outliers in the series, what do you suggest I do with them? – ankc Dec 09 '13 at 18:55

0 Answers0