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Structural learning with time‐varying components: tracking the cross‐section of financial time series
Author(s) -
Talih Makram,
Hengartner Nicolas
Publication year - 2005
Publication title -
journal of the royal statistical society: series b (statistical methodology)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 6.523
H-Index - 137
eISSN - 1467-9868
pISSN - 1369-7412
DOI - 10.1111/j.1467-9868.2005.00504.x
Subject(s) - graphical model , multivariate statistics , time series , computer science , stochastic volatility , covariance , bayesian probability , graph , artificial intelligence , econometrics , machine learning , mathematics , volatility (finance) , theoretical computer science , statistics
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.