Multivariate Bayesian forecasting models
This thesis concerns theoretical and practical Bayesian modelling of multivariate time series. Our main goal is to intruduce useful, flexible and tractable multivariate forecasting models and provide the necessary theory for their practical implementation. After a brief review of the dynamic linear model we formulate a new matrix-v-ariate generalization in which a significant part of the variance-covariance structure is unknown. And a new general algorithm, based on the sweep operator is provided for its recursive implementation. This enables important advances to be made in long-standing problems related with the specification of the variances. We address the problem of plug-in estimation and apply our results in the context of dynamic linear models. We extend our matrix-variate model by considering the unknown part of the variance-covariance structure to be dynamic. Furthermore, we formulate the dynamic recursive model which is a general counterpart of fully recursive econometric models. The latter part of the dissertation is devoted to modelling aspects. The usefulness of the methods proposed is illustrated with several examples involving real and simulated data.