Comparing Volatility in 2 populations

#1
Have got data for 2 populations and am wanting to compare the volatility/variability between them.

My initial thought was using a chi-squared (using an assumed value of 100 for the index) but not sure if this would be suitable/would work?

I've posted a summary plot of what I am using to give a better idea

Many thanks,
 
#3
Likelihood ratio test for the model allowing for different volatilities of the two time series (alternative hypothesis) versus a model enforcing the same volatility for the two time series (null hypothesis). Given scarcity of the data, the modeling framework can be simple AR(1).