The Markov approximation of the periodic multivariate Poisson autoregression
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866916673106214912 |
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| author | Khabou, Mahmoud Cohen, Edward A. K. Veraart, Almut E. D. |
| author_facet | Khabou, Mahmoud Cohen, Edward A. K. Veraart, Almut E. D. |
| contents | This paper introduces a periodic multivariate Poisson autoregression with potentially infinite memory, 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_02649 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Markov approximation of the periodic multivariate Poisson autoregression Khabou, Mahmoud Cohen, Edward A. K. Veraart, Almut E. D. Statistics Theory Probability This paper introduces a periodic multivariate Poisson autoregression with potentially infinite memory, 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. |
| title | The Markov approximation of the periodic multivariate Poisson autoregression |
| topic | Statistics Theory Probability |
| url | https://arxiv.org/abs/2504.02649 |