What quantities (means, betas) must be constant over time for the GRS test to be valid?

I am interested in testing the CAPM using the GRS test . Consider $N$ assets observed for $T$ time periods. Using the notation of Cochrane "Asset Pricing" (2005), the GRS test amounts to running $N$ time series regressions of the form R^{ei}_t=\alpha_i+\beta_i f_t+\varepsilon^i_t \tag{12.1} and testing the joint hypothesis $H_0\colon \alpha_1=\dots=\alpha_N=0$ . The $\alpha$ s are treated as pricing errors, so they better be zero if the CAPM is an adequate model. What quantities must be co