I have 10 time series on which I want to compare their volatility by using ARMA-GARCH models. I have estimated the ARMA-GARCH models by using eviews.
According to my supervisor now, I should compute the conditional coefficient of variation by dividing the conditional standard deviation to the conditional mean. As conditional mean takes both positive and negative values, I was wondering if I should take their absolute value. Negative coefficient of variation makes no sense, and then perform a $t$-test for means equality.
My thought is, why not to take the time series of the conditional standard deviation, make a descriptive statistics (in order to find the average st. dev.) and then perform a $t$-test of equality in means?