Poisson Autoregression

Konstantinos Fokianos (), Anders Rahbek and Dag Tjøstheim ()
Additional contact information
Konstantinos Fokianos: Department of Mathematics & Statistics, University of Cyprus, Postal: University of Cyprus
Dag Tjøstheim: Department of Mathematics, University of Bergen, Postal: University of Bergen

CREATES Research Papers from Department of Economics and Business Economics, Aarhus University

Abstract: This paper considers geometric ergodicity and likelihood based inference for linear and nonlinear Poisson autoregressions. In the linear case the conditional mean is linked linearly to its past values as well as the observed values of the Poisson process. This also applies to the conditional variance, making an interpretation as an integer valued GARCH process possible. In a nonlinear conditional Poisson model, the conditional mean is a nonlinear function of its past values and a nonlinear function of past observations. As a particular example an exponential autoregressive Poisson model for time series is considered. Under geometric ergodicity the maximum likelihood estimators of the parameters 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 non-perturbed versions vanish as far as the asymptotic distribution of the parameter estimates is concerned.

Keywords: asymptotic theory; count data; generalized linear models; geometric ergodicity; integer GARCH; likelihood; noncanonical link function; observation driven models; Poisson regression; ø-irreducibility. (search for similar items in EconPapers)
JEL-codes: C22 C51 (search for similar items in EconPapers)
Pages: 34
Date: 2009-03-24
New Economics Papers: this item is included in nep-ecm, nep-ets and nep-ore
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (124)

Downloads: (external link)
https://repec.econ.au.dk/repec/creates/rp/09/rp09_12.pdf (application/pdf)

Related works:
Journal Article: Poisson Autoregression (2009)
Working Paper: Poisson Autoregression (2008)
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:aah:create:2009-12

Access Statistics for this paper

More papers in CREATES Research Papers from Department of Economics and Business Economics, Aarhus University
Bibliographic data for series maintained by ().