Poisson Autoregression
Poisson Autoregression
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DOI：
10.1198/jasa.2009.tm08270
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发表时间：
2009-12-01
影响因子：
3.7
通讯作者：
Tjostheim, Dag
中科院分区：
文献类型：
--
作者：
Fokianos, Konstantinos;Rahbek, Anders;Tjostheim, Dag
在本文中，我们考虑线性和非线性Poisson自回归的几何遍历性和似然推断。在线性情况下，条件平均值与其过去的值以及泊松过程的观测值线性相关。这也适用于条件方差，使得解释为整值广义自回归条件异方差过程成为可能。在非线性条件泊松模型中，条件均值是其过去值和过去观测值的非线性函数。作为一个特例，我们考虑了时间序列的指数自回归泊松模型。在几何遍历条件下，证明了线性模型中的极大似然估计是渐近高斯的。此外，我们还给出了它们的渐近协方差矩阵的一致估计。我们通过马尔可夫理论和不可约性来验证几何遍历性。在最初的模型公式中，寻找证明遍历性的透明条件是一个微妙的问题。这个问题可以通过允许模型的摄动来绕过。我们证明了当扰动可以选择为任意小时，就参数估计的渐近分布而言，扰动版本和非扰动版本之间的差异消失了。这篇文章在网上有补充材料。
In this article we consider geometric ergodicity and likelihood-based inference for linear and nonlinear Poisson autoregression. In the linear case, the conditional mean is linked linearly to its past values, as well as to the observed values of the Poisson process. This also applies to the conditional variance, making possible interpretation as an integer-valued generalized autoregressive conditional heteroscedasticity process. In a nonlinear conditional Poisson model, the conditional mean is a nonlinear function of its past values and past observations. As a particular example, we consider an exponential autoregressive Poisson model for time series. Under geometric ergodicity, the maximum likelihood estimators are shown to be asymptotically Gaussian in the linear model. In addition, we provide a consistent estimator of their asymptotic covariance matrix. Our approach to verifying geometric ergodicity proceeds via Markov theory and irreducibility. Finding transparent conditions for proving ergodicity turns out to be a delicate problem in the original model formulation. This problem is circumvented by allowing a perturbation of the model. We show that as the perturbations can be chosen to be arbitrarily small, the differences between the perturbed and nonperturbed versions vanish as far as the asymptotic distribution of the parameter estimates is concerned. This article has supplementary material online.