Poisson autoregression

Fokianos, K. and Rahbek, A. and Tjøstheim, D. (2009) Poisson autoregression. Journal of the American Statistical Association, 104 (488). pp. 1430-1439. ISSN 0162-1459

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Abstract

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.

Item Type:
Journal Article
Journal or Publication Title:
Journal of the American Statistical Association
Uncontrolled Keywords:
/dk/atira/pure/subjectarea/asjc/1800/1804
Subjects:
?? φ IRREDUCIBILITYASYMPTOTIC THEORYCOUNT DATAGENERALIZED LINEAR MODELGEOMETRIC ERGODICITYINTEGER GENERALIZED AUTOREGRESSIVE CONDITIONAL HETEROSCEDASTICITYLIKELIHOODNONCANONICAL LINK FUNCTIONOBSERVATION-DRIVEN MODELPOISSON REGRESSIONSTATISTICS AND PROBABILIT ??
ID Code:
127816
Deposited By:
Deposited On:
01 Oct 2018 11:06
Refereed?:
Yes
Published?:
Published
Last Modified:
22 Sep 2023 00:36