# Comparing volatility among time series-GARCH Models

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.

1. 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.

2. 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?

To second your concern, Wikipedia's article on coefficient of variation ($c_v$) suggests that [t]he coefficient of variation should be computed only for data measured on a ratio scale rather than interval scale, as it is meaningless in the latter case. So you probably should not use it.
Now, how would you define the conditional coefficient of variation? Would you have one value per time point, like $c_{v,t}:=\frac{\sigma_t}{\mu_t}$? If you then try to remedy the problem of negative values by taking the absolute value, you would end up with a new measure $c^*_{v,t}:=\frac{\sigma_t}{|\mu_t|}$. It looks alright to me, just think whether it is exactly what you need (how exactly you define volatility).