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Some recent theory for autoregressive count time series

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  • Dag Tjøstheim

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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. Copyright Sociedad de Estadística e Investigación Operativa 2012

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  • Dag Tjøstheim, 2012. "Some recent theory for autoregressive count time series," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 21(3), pages 413-438, September.
  • Handle: RePEc:spr:testjl:v:21:y:2012:i:3:p:413-438
    DOI: 10.1007/s11749-012-0296-0
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    References listed on IDEAS

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    1. Douc, R. & Doukhan, P. & Moulines, E., 2013. "Ergodicity of observation-driven time series models and consistency of the maximum likelihood estimator," Stochastic Processes and their Applications, Elsevier, vol. 123(7), pages 2620-2647.
    2. Šárka Hudecová & Marie Hušková & Simos G. Meintanis, 2017. "Tests for Structural Changes in Time Series of Counts," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 44(4), pages 843-865, December.
    3. Pedro H. C. Sant’Anna, 2017. "Testing for Uncorrelated Residuals in Dynamic Count Models With an Application to Corporate Bankruptcy," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 35(3), pages 349-358, July.
    4. Scotto, Manuel G. & Weiß, Christian H. & Silva, Maria Eduarda & Pereira, Isabel, 2014. "Bivariate binomial autoregressive models," Journal of Multivariate Analysis, Elsevier, vol. 125(C), pages 233-251.

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