  This paper deals with inference and prediction for multiple correlated time
series, where one has also the choice of using a candidate pool of
contemporaneous predictors for each target series. Starting with a structural
model for the time-series, Bayesian tools are used for model fitting,
prediction, and feature selection, thus extending some recent work along these
lines for the univariate case. The Bayesian paradigm in this multivariate
setting helps the model avoid overfitting as well as capture correlations among
the multiple time series with the various state components. The model provides
needed flexibility to choose a different set of components and available
predictors for each target series. The cyclical component in the model can
handle large variations in the short term, which may be caused by external
shocks. We run extensive simulations to investigate properties such as
estimation accuracy and performance in forecasting. We then run an empirical
study with one-step-ahead prediction on the max log return of a portfolio of
stocks that involve four leading financial institutions. Both the simulation
studies and the extensive empirical study confirm that this multivariate model
outperforms three other benchmark models, viz. a model that treats each target
series as independent, the autoregressive integrated moving average model with
regression (ARIMAX), and the multivariate ARIMAX (MARIMAX) model.
