Monotone dependence in graphical models for multivariate Markov chains

摘要

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.