We derive strong mixing conditions for many existing discrete-valued time series models that include exogenous covariates in the dynamic. Our main contribution is to study how a condition on covariate process transfers response. Using coupling method, we first some Markov chains random environments, which gives result autoregressive categorical processes with strictly regressors. then extended ...

Abstract We develop a new Bayesian modelling framework for the class of higher-order, variable-memory Markov chains, and introduce an associated collection methodological tools exact inference with discrete time series. show that version context tree weighting alg-orithm can compute prior predictive likelihood exa-ctly (averaged over both models parameters), two related algorithms are introduce...