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Monotone Graphical Multivariate Markov Chains

In: Proceedings of COMPSTAT'2010

Author

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  • Roberto Colombi

    (University of Bergamo, Dept. of Information Technology and Math. Methods)

  • Sabrina Giordano

    (University of Calabria, Dept. of Economics and Statistics)

Abstract

In this paper, 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 non-causality, contemporaneous independence and monotone dependence coherent with a stochastic ordering. The tested hypotheses associated to a multi edge graph are proven to be equivalent to equality and inequality constraints on interactions of a multivariate logistic model parameterizing the transition probabilities. As the null hypothesis is specified by inequality constraints, the likelihood ratio statistic has chi-bar-square asymptotic distribution whose tail probabilities can be computed by simulation. The introduced hypotheses are tested on real categorical time series.

Suggested Citation

  • Roberto Colombi & Sabrina Giordano, 2010. "Monotone Graphical Multivariate Markov Chains," Springer Books, in: Yves Lechevallier & Gilbert Saporta (ed.), Proceedings of COMPSTAT'2010, pages 445-452, Springer.
    • Handle: RePEc:spr:sprchp:978-3-7908-2604-3_43
    DOI: 10.1007/978-3-7908-2604-3_43
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