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Poisson autoregression

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Poisson autoregression. / Fokianos, K.; Rahbek, A.; Tjøstheim, D.
In: Journal of the American Statistical Association, Vol. 104, No. 488, 2009, p. 1430-1439.

Research output: Contribution to Journal/MagazineJournal articlepeer-review

Harvard

Fokianos, K, Rahbek, A & Tjøstheim, D 2009, 'Poisson autoregression', Journal of the American Statistical Association, vol. 104, no. 488, pp. 1430-1439. https://doi.org/10.1198/jasa.2009.tm08270

APA

Fokianos, K., Rahbek, A., & Tjøstheim, D. (2009). Poisson autoregression. Journal of the American Statistical Association, 104(488), 1430-1439. https://doi.org/10.1198/jasa.2009.tm08270

Vancouver

Fokianos K, Rahbek A, Tjøstheim D. Poisson autoregression. Journal of the American Statistical Association. 2009;104(488):1430-1439. doi: 10.1198/jasa.2009.tm08270

Author

Fokianos, K. ; Rahbek, A. ; Tjøstheim, D. / Poisson autoregression. In: Journal of the American Statistical Association. 2009 ; Vol. 104, No. 488. pp. 1430-1439.

Bibtex

@article{152a7c17ddcb4b8d89c7fadb4be08980,
title = "Poisson autoregression",
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.",
keywords = "φ irreducibility, Asymptotic theory, Count data, Generalized linear model, Geometric ergodicity, Integer generalized autoregressive conditional heteroscedasticity, Likelihood, Noncanonical link function, Observation-driven model, Poisson regression",
author = "K. Fokianos and A. Rahbek and D. Tj{\o}stheim",
year = "2009",
doi = "10.1198/jasa.2009.tm08270",
language = "English",
volume = "104",
pages = "1430--1439",
journal = "Journal of the American Statistical Association",
issn = "0162-1459",
publisher = "Taylor and Francis Ltd.",
number = "488",

}

RIS

TY - JOUR

T1 - Poisson autoregression

AU - Fokianos, K.

AU - Rahbek, A.

AU - Tjøstheim, D.

PY - 2009

Y1 - 2009

N2 - 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.

AB - 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.

KW - φ irreducibility

KW - Asymptotic theory

KW - Count data

KW - Generalized linear model

KW - Geometric ergodicity

KW - Integer generalized autoregressive conditional heteroscedasticity

KW - Likelihood

KW - Noncanonical link function

KW - Observation-driven model

KW - Poisson regression

U2 - 10.1198/jasa.2009.tm08270

DO - 10.1198/jasa.2009.tm08270

M3 - Journal article

VL - 104

SP - 1430

EP - 1439

JO - Journal of the American Statistical Association

JF - Journal of the American Statistical Association

SN - 0162-1459

IS - 488

ER -