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Some recent theory for autoregressive count time series

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Abstract

In this paper an overview is given over recent theoretical developments in autoregressive count time series. The focus is on generalized autoregressive models where the autoregressive structure is incorporated via a link function. Starting from an ordinary autoregressive model the difficulties in extending standard theory of statistical inference to count time series are highlighted. Special attention is given to the issues of ergodicity and asymptotic theory of estimation. Two main approaches are mentioned, a perturbation approach and the use of a weak dependence concept. The main emphasis is on the former. Linear as well as log-linear and nonlinear models are treated. It is argued that the developed theory forms a necessary basis for modelling and application of these count time series. The setting of the paper is one of simple models and conditional distributions of Poisson type. But it is claimed that the framework is general enough to handle many extensions with an accompanying flexibility in applications of these models.

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Acknowledgement

I am grateful to the editor and to three referees for a number of valuable remarks on an earlier version.

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  1. Department of Mathematics, University of Bergen, Johs. Brunsgt. 12, 5008, Bergen, Norway

    Dag Tjøstheim

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  1. Dag Tjøstheim
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Correspondence to Dag Tjøstheim.

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Tjøstheim, D. Some recent theory for autoregressive count time series. TEST 21, 413–438 (2012). https://doi.org/10.1007/s11749-012-0296-0

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