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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Research output: Contribution to Journal/Magazine › Journal article › peer-review
Research output: Contribution to Journal/Magazine › Journal article › peer-review
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TY - JOUR
T1 - On categorical time series with covariates
AU - Fokianos, Konstantinos
AU - Truquet, Lionel
N1 - 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
PY - 2019/9/1
Y1 - 2019/9/1
N2 - 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.
AB - 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.
KW - Autoregression
KW - Categorical data
KW - Chains with complete connection
KW - Coupling
KW - Covariates
KW - Ergodicity
KW - Markov chains
U2 - 10.1016/j.spa.2018.09.012
DO - 10.1016/j.spa.2018.09.012
M3 - Journal article
VL - 129
SP - 3446
EP - 3462
JO - Stochastic Processes and their Applications
JF - Stochastic Processes and their Applications
SN - 0304-4149
IS - 9
ER -