Variance estimation for multivariate normal dynamic linear models

In multivariate normal dynamic and state-space linear models the observational variance matrix is usually assumed known. Apart from a handful of special cases, estimation procedures that allow for the variance of the observational errors to be left unspecified are not widely available. The foundation of this paper is the general multivariate normal dynamic linear model with unknown but fixed observational variances. We propose a novel variance estimator that does not use any prior Wishart distribution, and derive the first two moments of the prior, posterior, and forecast distributions, unconditional of the observation variance matrix. Simulation studies demonstrate the validity of our estimation algorithm, as well as its computational advantages over a competing Markov chain Monte Carlo approach. The examples discussed include bivariate local level and linear growth dynamic models.