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On categorical time series models with covariates

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  • Fokianos, Konstantinos
  • Truquet, Lionel

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.

Suggested Citation

  • Fokianos, Konstantinos & Truquet, Lionel, 2019. "On categorical time series models with covariates," Stochastic Processes and their Applications, Elsevier, vol. 129(9), pages 3446-3462.
    • Handle: RePEc:eee:spapps:v:129:y:2019:i:9:p:3446-3462
    DOI: 10.1016/j.spa.2018.09.012
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    2. Adriano Zanin Zambom & Seonjin Kim & Nancy Lopes Garcia, 2022. "Variable length Markov chain with exogenous covariates," Journal of Time Series Analysis, Wiley Blackwell, vol. 43(2), pages 312-328, March.
    3. Fokianos, Konstantinos & Fried, Roland & Kharin, Yuriy & Voloshko, Valeriy, 2022. "Statistical analysis of multivariate discrete-valued time series," Journal of Multivariate Analysis, Elsevier, vol. 188(C).

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