When modelling multivariate financial data, the problem of structural learning becomes compounded by the fact that the covariance structure changes with time. Previous work has focused on modelling those changes using multivariate stochastic volatility models or multivariate auto-regressive heteroskedacity models. In this thesis we present an alternative to these models that focuses instead on the latent graphical structure related to the precision matrix. The precision matrix proves to be a natural parameterization in the multivariate Normal model. It is intimately related to the coefficients in the simultaneous regression of each variable on all of the remaining ones. This thesis develops a graphical model for sequences of Gaussian random vectors when changes in the underlying graph—which is specified by zeroes in the precision matrix—occur at random times, and a new block of data is created with the addition or deletion of an edge. We show how a Bayesian hierarchical model incorporates both the uncertainty about that graph, and the time-variation thereof. Our main objective is to learn the graph underlying the last, most current, block of data. In fact, our Bayesian framework allows us to make inference about the whole history up to and including the last block.
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