Mixing properties of non‐stationary multi‐variate count processes

Zinsou Max Debaly, Michael H. Neumann and Lionel Truquet

Journal of Time Series Analysis, 2025, vol. 46, issue 3, 552-581

Abstract: We consider multi‐variate versions of two popular classes of integer‐valued processes. While the transition mechanism is time‐homogeneous, a possible non‐stationarity is introduced by an exogeneous covariate process. We prove absolute regularity (β$$ \beta $$‐mixing) for the count process with exponentially decaying mixing coefficients. The proof of this result makes use of some sort of contraction in the transition mechanism which allows a coupling of two versions of the count process such that they eventually coalesce. We show how this result can be used to prove asymptotic normality of a least squares estimator of an involved model parameter.

Date: 2025
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https://doi.org/10.1111/jtsa.12775

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