Monotone dependence in graphical models for multivariate Markov chains

Roberto Colombi () and Sabrina Giordano ()

Metrika: International Journal for Theoretical and Applied Statistics, 2013, vol. 76, issue 7, 873-885

Abstract: We show that a deeper insight into the relations among marginal processes of a multivariate Markov chain can be gained by testing hypotheses of Granger noncausality, contemporaneous independence and monotone dependence. Granger noncausality and contemporaneous independence conditions are read off a mixed graph, and the dependence of an univariate component of the chain on its parents—according to the graph terminology—is described in terms of stochastic dominance criteria. The examined hypotheses are proven to be equivalent to equality and inequality constraints on some parameters of a multivariate logistic model for the transition probabilities. The introduced hypotheses are tested on real categorical time series. Copyright Springer-Verlag Berlin Heidelberg 2013

Keywords: Granger causality; Conditional independence; Stochastic orderings; Order-restricted inference; Chi-bar-square distribution (search for similar items in EconPapers)
Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:spr:metrik:v:76:y:2013:i:7:p:873-885

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DOI: 10.1007/s00184-012-0421-9

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