I am currently writing a paper on asymmetric volatility modeling of brent, gold, silver, wheat, soybean and corn from 1986-2012 and divided them into 4 sub-sample periods (i.e. 1986-1991, 1991-1997, 1997-2005, 2005-2012 and where the no. of observations are: 1515, 1515, 2000, 2000, respectively) and I have some questions to ask regarding it. I hope you guys can help me out here. Thank you so much.
A summary of what I have done so far: - Box.test on squared returns and ARCH-LM tests for conditional heteroskedasticity. If null is rejected, I proceed with GARCH(1,1) modeling
Using the rugarch package, if sign bias test (based on paper done by Engle and Ng - http://www.jstor.org/discover/10.2307/2329066?uid=3738992&uid=2129&uid=2&uid=70&uid=4&sid=21101646509647) is statistically significant then I propose three asymmetric vol models (i.e. EGARCH(1,1), GJR-GARCH(1,1) and APARCH(1,1), d=1)
The final model is then chosen based on BIC, Q-statistics on standardized residuals and its squared terms and ARCH LM tests across 4 distributions (i.e. norm, std, sstd and ged)
My questions are:
If the gamma coefficient (leverage effect) of GJR is insignificant but the news impact curve show that negative return shocks does induce greater increment in conditional variance than positive return shocks and the sign bias test from GARCH(1,1) is significant and model checks deem the GJR model suitable for this particular period then how should one conclude on news impact and leverage effect for this period? Does it mean a better model can be proposed for it?
Related to question 1., if leverage effect, alphas and betas are insignificant but model checks suggest that this model is indeed suitable. What can we conclude from it and how can we improve the model? Since alphas and betas are insignificant, what can we say about its persistence and unconditional variance? Are they still statistically meaningful?
Amongst all the models, there is one particular model - APARCH(1,1) for wheat (2nd sub-sample) has a persistence of 0.8ish and theoretically, this just means its rate of decay is higher as compared to the rest. But apart from this, are there any more information that we can glean from the result?
The QQ-plots for all sub-samples for corn, using GARCH(1,1) with ged show that it's a terrible fit and presence of quite a number of outliers. But its coefficients are significant and BIC value is the lowest compared to the other 3 distributions. However, the QQ-plot of std shows a much better fit. I suspect there's convergence problem with ged distribution. How can we prevent that or should just stick to std distribution?
If ARCH test conducted before GARCH(1,1) was modeled fail to reject null, what can we do about modeling the volatility without including more data points?
Your help is greatly appreciated. Thank you!