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