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This paper introduces a new multivariate model, dubbed Generalized Conditional Autoregressive Beta (GCAB) GARCH, for jointly modeling the time-varying slope coefficients in a multiple regression conditionally heteroskedastic system. The model, which implies a structure tailored to the linear asset pricing framework, allows the coexistence of constant and time-varying betas, simplifies testing (or imposing) cross-sectional restrictions and, introduces new mechanisms of propagation of shocks, namely beta spillovers, in a coherent, explicit and parsimonious way. We derive conditions for
stationarity and uniform invertibility and, to mitigate the problem of parameter proliferation in large dimensions, we provide estimators for beta and covariance tracking. We propose a variety of parallel and sequential maximum likelihood estimators and, we investigate their finite sample properties of by means of extensive Monte Carlo experiments. Finally, the GCAB is used in the Fama-French three factors asset pricing framework using real data.
