On Categorical Time Series Models With Covariates

摘要: We study the problem of stationarity and ergodicity for autoregressive multinomial logistic time series models which possibly include a latent process are defined by GARCH-type recursive equation. improve considerably upon existing results related to conditions such models. Proofs based on theory developed chains with complete connections. This approach is useful coupling technique utilized studying more general finite-state stochastic processes. Such processes generalize Markov assuming infinite order past values. For finite chains, we also discuss properties when some strongly exogenous covariates considered in dynamics process.