Forecast covariances in the linear multiregression dynamic model

The linear multiregression dynamic model (LMDM) is a Bayesian dynamic model which preserves any conditional independence and causal structure across a multivariate time series. The conditional independence structure is used to model the multivariate series by separate (conditional) univariate dynamic linear models, where each series has contemporaneous variables as regressors in its model. Calculating the forecast covariance matrix (which is required for calculating forecast variances in the LMDM) is not always straightforward in its current formulation. In this paper we introduce a simple algebraic form for calculating LMDM forecast covariances. Calculation of the covariance between model regression components can also be useful and we shall present a simple algebraic method for calculating these component covariances. In the LMDM formulation, certain pairs of series are constrained to have zero forecast covariance. We shall also introduce a possible method to relax this restriction.