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Alternative distributions for observation driven count series models

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  • Drescher, Daniel
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    Abstract

    Observation-driven models provide a flexible framework for modelling time series of counts. They are able to capture a wide range of dependence structures. Many applications in this field of research are concerned with count series whose conditional distribution given past observations and explanatory variables is assumed to follow a Poisson distribution. This assumption is very convenient since the Poisson distribution is simple and leads to models which are easy to implement. On the other hand this assumption is often too restrictive since it implies equidispersion, the fact that the conditional mean equals the conditional variance. This assumption is often violated in empirical applications. Therefore more flexible distributions which allow for overdispersion or underdispersion should be used. This paper is concerned with the use of alternative distributions in the framework of observationdriven count series models. In this paper different count distributions and their properties are reviewed and used for modelling. The models under consideration are applied to a time series of daily counts of asthma presentations at a Sydney hospital. This data set has already been analyzed by Davis et al. (1999, 2000). The Poisson-GLARMA model proposed by these authors is used as a benchmark. This paper extends the work of Davis et al. (1999) to distributions which are nested in either the generalized negative binomial or the generalized Poisson distribution. Additionally the maximum likelihood estimation for observation-driven models with generalized distributions is presented in this paper. --

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    File URL: http://econstor.eu/bitstream/10419/21999/1/EWP-2005-11.pdf
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    Bibliographic Info

    Paper provided by Christian-Albrechts-University of Kiel, Department of Economics in its series Economics Working Papers with number 2005,11.

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    Date of creation: 2005
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    Handle: RePEc:zbw:cauewp:3197

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    Related research

    Keywords: Count series; observation-driven models; GLARMA; dicrete distributions;

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    1. Saha, Atanu & Dong, Diangsheng, 1997. "Estimating Nested Count Data Models," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 59(3), pages 423-30, August.
    2. Winfried Pohlmeier & Roman Liesenfeld, 2003. "A Dynamic Integer Count Data Model for Financial Transaction Prices," CoFE Discussion Paper 03-03, Center of Finance and Econometrics, University of Konstanz.
    3. Tina Hviid Rydberg & Neil Shephard, 2002. "Dynamics of trade-by-trade price movements: decomposition and models," OFRC Working Papers Series 2002fe04, Oxford Financial Research Centre.
    4. Cameron, A Colin & Trivedi, Pravin K, 1986. "Econometric Models Based on Count Data: Comparisons and Applications of Some Estimators and Tests," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 1(1), pages 29-53, January.
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