Graphical models for multivariate Markov chains
The aim of this paper is to provide a graphical representation of the dynamic relations among the marginal processes of a first order multivariate Markov chain. We show how to read Granger-noncausal and contemporaneous independence relations off a particular type of mixed graph, when directed and bi-directed edges are missing. Insights are also provided into the Markov properties with respect to a graph that are retained under marginalization of a multivariate chain. Multivariate logistic models for transition probabilities are associated with the mixed graphs encoding the relevant independencies. Finally, an application on real data illustrates the methodology.
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Volume (Year): 107 (2012)
Issue (Month): C ()
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References listed on IDEAS
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- Monia Lupparelli & Giovanni M. Marchetti & Wicher P. Bergsma, 2009. "Parameterizations and Fitting of Bi-directed Graph Models to Categorical Data," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 36(3), pages 559-576.
- Joseph B. Lang, 2005. "Homogeneous Linear Predictor Models for Contingency Tables," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 121-134, March.
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- Eichler, Michael, 2007. "Granger causality and path diagrams for multivariate time series," Journal of Econometrics, Elsevier, vol. 137(2), pages 334-353, April.
- Christian Gouriéroux & Alain Monfort & Eric Renault, 1987. "Kullback Causality Measures," Annals of Economics and Statistics, GENES, issue 6-7, pages 369-410.
- repec:adr:anecst:y:1987:i:6-7 is not listed on IDEAS
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