Structural learning with time-varying components: tracking the cross-section of financial time series

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Abstract:

Summary. 

When modelling multivariate financial data, the problem of structural learning is compounded by the fact that the covariance structure changes with time. Previous work has focused on modelling those changes by using multivariate stochastic volatility models. We present an alternative to these models that focuses instead on the latent graphical structure that is related to the precision matrix. We develop a graphical model for sequences of Gaussian random vectors when changes in the underlying graph 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.

Keywords: Covariance selection; Dynamic graphical model; Markov chain Monte Carlo methods; Markov random field; Multivariate stochastic volatility; Precision matrix

Document Type: Research Article

DOI: http://dx.doi.org/10.1111/j.1467-9868.2005.00504.x

Affiliations: 1: Hunter College of the City University of New York, USA 2: Los Alamos National Laboratory, USA

Publication date: June 1, 2005

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