The Markov approximation of the periodic multivariate Poisson autoregression
File(s)
Published version
Author(s)
Khabou, Mahmoud
Cohen, Edward
Veraart, Almut
Type
Journal Article
Abstract
This paper introduces a periodic multivariate Poisson autoregression with potentially an infinite number of lags, with a special focus on the network setting. Using contraction techniques, we study the stability of such a process and provide upper bounds on how fast it reaches the periodically stationary regime. We then propose a computationally efficient Markov approximation using the properties of the exponential function and a density result. Furthermore, we prove the strong consistency of the maximum likelihood estimator for the Markov approximation and empirically test its robustness in the case of misspecification. Our model is applied to the prediction of weekly Rotavirus cases in Berlin, demonstrating superior performance compared to the existing PNAR model.
Date Issued
2025-04-01
Date Acceptance
2026-02-09
Citation
Electronic Journal of Statistics, 2025, 20 (1), pp.862-914
ISSN
1935-7524
Publisher
Institute of Mathematical Statistics
Start Page
862
End Page
914
Journal / Book Title
Electronic Journal of Statistics
Volume
20
Issue
1
Copyright Statement
Copyright © 2025 The Author(s). This work is licensed under a Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0/).
License URL
Identifier
10.1214/26-EJS2500
Subjects
MSC2020 subject classifications: Primary 62M10; secondary 62F12 Multi-variate count time series
periodicity
Markov approximation
likelihood estimation
Publication Status
Published
Date Publish Online
2026-03-04