Periodic stationarity conditions for mixture periodic INGARCH models

Bader S. Almohaimeed; Bader S. Almohaimeed

doi:10.3934/math.2022546

AIMS Mathematics

2022, Volume 7, Issue 6: 9809-9824. doi: 10.3934/math.2022546

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Research article

Periodic stationarity conditions for mixture periodic INGARCH models

Bader S. Almohaimeed ^,

Department of Mathematics, College of Science, Qassim University, Saudi Arabia
Correction on: AIMS Mathematics 7: 18280–18281

Received: 19 December 2021 Revised: 06 February 2022 Accepted: 16 February 2022 Published: 18 March 2022
MSC : 37A25, 60A10, 60G10, 60H35, 62M10, 62M20

This paper proposes strict periodic stationarity and periodic ergodicity conditions for a finite mixture integer-valued GARCH model with $ S $-periodic time-varying parameters that depend on the state of an independent and periodically distributed regime sequence. In this model, the past conditional mean values depend on the past of the regime variable in the same order, so the model is characterized by path-regime dependence. We also propose sufficient conditions for periodic stationarity when the conditional means are nonlinear of past observations. The results are applied to various discrete conditional distributions.
- integer-valued time series models,
- finite mixture models,
- periodic time-varying models,
- ergodic properties,
- path dependence
Citation: Bader S. Almohaimeed. Periodic stationarity conditions for mixture periodic INGARCH models[J]. AIMS Mathematics, 2022, 7(6): 9809-9824. doi: 10.3934/math.2022546

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Abstract

This paper proposes strict periodic stationarity and periodic ergodicity conditions for a finite mixture integer-valued GARCH model with $ S $-periodic time-varying parameters that depend on the state of an independent and periodically distributed regime sequence. In this model, the past conditional mean values depend on the past of the regime variable in the same order, so the model is characterized by path-regime dependence. We also propose sufficient conditions for periodic stationarity when the conditional means are nonlinear of past observations. The results are applied to various discrete conditional distributions.

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