# In-sample forecast accuracy of Beta (Kalman filter) CAPM

One can calculate time-varying betas (known from the CAPM) using the Kalman filter. For example, one can calculate the in-sample forecast accuracy using the MAE.

$$MAE = \frac{1}{T}\sum_{t=1}^T|\hat{R}_{t}-R_{t}|$$

This compares the actual return with the estimated return. The estimated return $$\hat{R}_{t}$$ is the product of the calculated beta and the actual market return $$R_{mt}$$.

$$\hat{R}_{t}=\hat{\beta}_{t}R_{mt}$$

I would like to know if the betas used for comparison here would have to be filtered betas or predicted betas? In the papers you often see these tests, but it is never stated whether they are the filtered values or predictions (one-steap ahead forecast).

I am very appreciative of any help.