  This paper develops a Bayesian procedure for estimation and forecasting of
the volatility of multivariate time series. The foundation of this work is the
matrix-variate dynamic linear model, for the volatility of which we adopt a
multiplicative stochastic evolution, using Wishart and singular multivariate
beta distributions. A diagonal matrix of discount factors is employed in order
to discount the variances element by element and therefore allowing a flexible
and pragmatic variance modelling approach. Diagnostic tests and sequential
model monitoring are discussed in some detail. The proposed estimation theory
is applied to a four-dimensional time series, comprising spot prices of
aluminium, copper, lead and zinc of the London metal exchange. The empirical
findings suggest that the proposed Bayesian procedure can be effectively
applied to financial data, overcoming many of the disadvantages of existing
volatility models.
