期刊
STOCHASTIC PROCESSES AND THEIR APPLICATIONS
卷 129, 期 9, 页码 3446-3462出版社
ELSEVIER
DOI: 10.1016/j.spa.2018.09.012
关键词
Autoregression; Categorical data; Chains with complete connection; Coupling; Covariates; Ergodicity; Markov chains
We study the problem of stationarity and ergodicity for autoregressive multinomial logistic time series models which possibly include a latent process and are defined by a GARCH-type recursive equation. We improve considerably upon the existing conditions about stationarity and ergodicity of those models. Proofs are based on theory developed for chains with complete connections. A useful coupling technique is employed for studying ergodicity of infinite order finite-state stochastic processes which generalize finite-state Markov chains. Furthermore, for the case of finite order Markov chains, we discuss ergodicity properties of a model which includes strongly exogenous but not necessarily bounded covariates. (C) 2018 Elsevier B.V. All rights reserved.
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