I am doing a research project where I am examining the effect that Covid-19 has had on the returns and volatility of the financial markets. I have opted to use a GJR-GARCH-M (1,1) model to properly account for the leverage effect. I have purposely avoided using EGARCH and other asymmetric GARCH models because GJR is less explored in this context.
I am accounting for stock market volatility using 10 market indices for different countries, then I am taking my "volatility" to be ln(P_t/P_(t-1)), where P_t is the closing price of a particular index on day t, as specified in a number of different academic papers and text books (e.g. Brooks). Other independent variables I have currently collected are daily Covid-19 case data (cases and deaths) on a country-specific and global level. The Government Response Index from Oxford Covid Government Response Tracker which gives a measure of how stringent a particular government's covid measures have been (e.g. school closures, social distancing restrictions etc). Data has all been pre-formatted in Excel so that the dates all properly align and missing values (e.g. stock market holidays) were filled in using previous available value to ensure comparability cross-country.
As suggested in Brooks (2019) I ran an OLS regression of my "volatility" on all of my independent variables and then checked the correlogram of squared residuals which indicated presence of ARCH effects (All P-values zero up to 36 lags).
My current settings within EViews for GJR-GARCH-M are all "standard" apart from I selected 'EViews Legacy' - which was a recommendation I picked up at some point for GJR-GARCH but cannot remember where. I have also selected my error distribution as t-distribution since Jarque-Bera test indicated non-normality and financial time series generally exhibit fatter tails.
There are two issues I would like to address. Firstly, when running my GJR-GARCH regressions, nearly all of my ARCH effect terms have negative coefficients, this is obviously a problem since it breaches the non-negativity constraints requirements. Although in most cases, the ARCH term is not statistically significant, so I figured this actually wasn't an issue (see Screenshot 1). However, there are some cases where the ARCH term is negative and significant, which is a problem (see Screenshot 2). All GARCH effect terms and leverage terms are positive, and the majority are significant. What do you make of the negative ARCH effect coefficients?
Secondly, I want to ensure that my findings are robust, which I would ideally like to do by including more country-specific regressors. However, in nearly all academic literature I have seen, there is usually a maximum of one exogenous regressor included in the conditional mean and/or variance equation. I have seen a couple of papers where they conduct a GJR-GARCH without any exogenous regressors and then generate a GARCH variance series and use that in an OLS regression - but that instinctively feels wrong to me? What is the appropriate way to control for country specific effects in this context? I seem to find that if I include several exogenous regressors the GJR-GARCH model encounters similar issues as I have described above (e.g. significant negative ARCH effect coefficient - see Screenshot 3).
If anyone is able to provide additional clarification that would be great, or point me towards additional resources. I have looked at so many different papers and textbooks and am still none the wiser. Please let me know if I have been unclear anywhere or forgotten to mention something!
For technical questions regarding estimation of single equations, systems, VARs, Factor analysis and State Space Models in EViews. General econometric questions and advice should go in the Econometric Discussions forum.
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