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  • 1709.09372

    Rights statement: This is the author’s version of a work that was accepted for publication in Stochastic Processes and their Applications. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Stochastic Processes and their Applications, 129, 9, 2019 DOI: 10.1016/j.spa.2018.09.012

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On categorical time series with covariates

Research output: Contribution to journalJournal article

Published
<mark>Journal publication date</mark>1/09/2019
<mark>Journal</mark>Stochastic Processes and their Applications
Issue number9
Volume129
Number of pages17
Pages (from-to)3446-3462
Publication statusPublished
Early online date9/10/18
Original languageEnglish

Abstract

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.

Bibliographic note

This is the author’s version of a work that was accepted for publication in Stochastic Processes and their Applications. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Stochastic Processes and their Applications, 129, 9, 2019 DOI: 10.1016/j.spa.2018.09.012