Title: The Markov approximation of the periodic multivariate Poisson autoregression Show Chinese title

Title: 周期多变量泊松自回归的马尔可夫近似

Abstract: 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. Show Chinese abstract

Abstract: 本文介绍了一种带有潜在无限记忆的周期性多元泊松自回归模型，并特别关注网络设定。利用收缩技术，我们研究了此类过程的稳定性，并提供了其达到周期平稳状态的速度上限。随后，我们基于指数函数的性质和一个密度结果，提出了一个计算效率高的马尔可夫近似方法。此外，我们证明了马尔可夫近似下最大似然估计量的强一致性，并在误设情况下对其鲁棒性进行了实证检验。我们的模型被应用于预测柏林每周轮状病毒病例，显示出比现有PNAR模型更优越的性能。