Stability conditions for heteroscedastic factor models with conditionally autoregressive betas

We characterize the stability properties of a heteroscedastic multi‐factor model of financial asset returns, with conditionally known factors and beta coefficients driven by general conditionally autoregressive processes. These processes generalize existing structures and address a number of empirical issues of current concern. Our analysis derives closed‐form sufficient conditions for the existence of strict stationary solutions for the composite asset conditional variances and covariances, not known previously in the literature. It is shown that stability is guaranteed when individual‐process and cross‐process restrictions hold simultaneously. Our results are also applicable to the study of the co‐movement between volatility and beta coefficients as well as between beta coefficients themselves.