Maximum likelihood estimation of a TVP-VAR

Abstract This paper proposes the maximum likelihood estimation of a vector autoregression with drifting coefficients and multivariate stochastic volatility. The coefficients are assumed to follow heteroscedastic random walks and the volatility of the system is modeled as a Wishart process, increasing the flexibility in describing the behavior of stochastic covariances. Exploiting the conjugacy between Normal, Wishart and multivariate beta distributions, filtering formulas for tracking the latent states and expression for the likelihood function can be obtained in closed form.