I worked in Mutual Fund and have been worked in these fields more than 4 years

In my experience, Beta is now good to describe market risk for the following reason:

it is not steady. for example the demension you used, 40 trading daily data? 5 years monthly data?

the second, moving Beta or Unique one?

Our Market Beta stays in one narrow range{0.7-1.2}.

The Problem using AR(2) is that you used stable process, but the data are not, it is the KEY of your problem.

Care!