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February 2022 Mixing properties of non-stationary INGARCH(1,1) processes
Paul Doukhan, Anne Leucht, Michael H. Neumann
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Bernoulli 28(1): 663-688 (February 2022). DOI: 10.3150/21-BEJ1362

Abstract

We derive mixing properties for a broad class of Poisson count time series satisfying a certain contraction condition. Using specific coupling techniques, we prove absolute regularity at a geometric rate not only for stationary Poisson-GARCH processes but also for models with an explosive trend. We provide easily verifiable sufficient conditions for absolute regularity for a variety of models including classical (log-)linear models. Finally, we illustrate the practical use of our results for hypothesis testing.

Funding Statement

This work was funded by CY Initiative of Excellence (grant “Investissements d’Avenir” ANR-16-IDEX-0008) Project “EcoDep” PSI-AAP2020-0000000013 (first and third authors) and within the MME-DII center of excellence (ANR-11-LABEX-0023-01), and the Friedrich Schiller University in Jena (for the first author).

Acknowledgments

We thank two anonymous referees for their valuable comments that led to a significant improvement of the paper.

Citation

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Paul Doukhan. Anne Leucht. Michael H. Neumann. "Mixing properties of non-stationary INGARCH(1,1) processes." Bernoulli 28 (1) 663 - 688, February 2022. https://doi.org/10.3150/21-BEJ1362

Information

Received: 1 November 2020; Revised: 1 April 2021; Published: February 2022
First available in Project Euclid: 10 November 2021

Digital Object Identifier: 10.3150/21-BEJ1362

Keywords: absolute regularity , coupling , INGARCH , Mixing

Rights: Copyright © 2022 ISI/BS

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Vol.28 • No. 1 • February 2022
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