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Maximum Likelihood Estimation for an Observation Driven Model for Poisson Counts

Author

Listed:
  • Richard A. Davis

    (Colorado State University)

  • William T. M. Dunsmuir

    (University of New South Wales)

  • Sarah B. Streett

    (National Institute of Standards and Technology)

Abstract

This paper is concerned with an observation-driven model for time series of counts whose conditional distribution given past observations follows a Poisson distribution.This class of models is capable of modeling a wide range of dependence structures and is readily estimated using an approximation to the likelihood function. Recursive formulae for carrying out maximum likelihood estimation are provided and the technical components required for establishing a central limit theorem of the maximum likelihood estimates are given in a special case.

Suggested Citation

  • Richard A. Davis & William T. M. Dunsmuir & Sarah B. Streett, 2005. "Maximum Likelihood Estimation for an Observation Driven Model for Poisson Counts," Methodology and Computing in Applied Probability, Springer, vol. 7(2), pages 149-159, June.
    • Handle: RePEc:spr:metcap:v:7:y:2005:i:2:d:10.1007_s11009-005-1480-4
    DOI: 10.1007/s11009-005-1480-4
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    Cited by:

    1. Rainer Baule & Bart Frijns & Sebastian Schlie, 2024. "Feedback Trading: The Intraday Case of Retail Derivatives," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 44(9), pages 1487-1507, September.
    2. Blazsek, Szabolcs & Escribano, Alvaro, 2016. "Score-driven dynamic patent count panel data models," Economics Letters, Elsevier, vol. 149(C), pages 116-119.
    3. Ryoko Ito, 2016. "Asymptotic Theory for Beta-t-GARCH," Cambridge Working Papers in Economics 1607, Faculty of Economics, University of Cambridge.
    4. Blazsek, Szabolcs, 2015. "Dynamic conditional score patent count panel data models," UC3M Working papers. Economics we1510, Universidad Carlos III de Madrid. Departamento de Economía.
    5. Marinho G. Andrade & Katiane S. Conceição & Nalini Ravishanker, 2024. "Zero-modified count time series modeling with an application to influenza cases," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 108(3), pages 611-637, September.
    6. Doukhan, Paul & Fokianos, Konstantinos & Tjøstheim, Dag, 2012. "On weak dependence conditions for Poisson autoregressions," Statistics & Probability Letters, Elsevier, vol. 82(5), pages 942-948.
    7. Alj, Abdelkamel & Azrak, Rajae & Mélard, Guy, 2014. "On conditions in central limit theorems for martingale difference arrays," Economics Letters, Elsevier, vol. 123(3), pages 305-307.
    8. Giovanni Angelini & Giuseppe Cavaliere & Enzo D'Innocenzo & Luca De Angelis, 2022. "Time-Varying Poisson Autoregression," Papers 2207.11003, arXiv.org.
    9. Konstantinos Fokianos, 2012. "Comments on: 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 451-454, September.
    10. Abdelkamel Alj & Rajae Azrak & Guy Melard, 2014. "On Conditions in Central Limit Theorems for Martingale Difference Arrays Long Version," Working Papers ECARES ECARES 2014-05, ULB -- Universite Libre de Bruxelles.

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