Some conditional independencies in bivariate categorical time series

Abstract

In this work we consider two time series of categorical data as a bivariate Markov chain. The markovianity assumption allows us to simplify some conditional independencies introduced in order to describe if the knowledge of past or present realizations of one of the two categorical variables can provide some additional information to forecast the current realization of the other. The three simple conditions introduced here, though referring only to the recent realizations of the two variables, imply the more general conditions defined by all of the past realizations. Moreover, we show that the proposed conditions are equivalent to the hypothesis of null coefficients in some parametric models for joint transition probabilities. Finally, we represent these conditions in terms of missing edges in chain graphs.