If I have 24 temporal covariance matrices (say monthly covariance matrices computed from daily returns of all the SP500 stocks), and I compute 24 betas for variables x and y for every month for past 2 years. Then,
- What is then the best estimator of beta (e.g. equally or exponentially weighted average of these betas?
- How can I analyse the stability/variability of the individual beta as well as the estimator of the beta?
- By looking at these monthly betas can I make any conclusions of the relationship between x & y?
I would very much appreciate, if you have any standard references that clarify my concerns.