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Markov Poisson regression models for discrete time series. Part 1: Methodology

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  • Peiming Wang
  • Martin Puterman

Abstract

This paper proposes and investigates a class of Markov Poisson regression models in which Poisson rate functions of covariates are conditional on unobserved states which follow a finite-state Markov chain. Features of the proposed model, estimation, inference, bootstrap confidence intervals, model selection and other implementation issues are discussed. Monte Carlo studies suggest that the proposed estimation method is accurate and reliable for single- and multiple-subject time series data; the choice of starting probabilities for the Markov process has little eff ect on the parameter estimates; and penalized likelihood criteria are reliable for determining the number of states. Part 2 provides applications of the proposed model.

Suggested Citation

  • Peiming Wang & Martin Puterman, 1999. "Markov Poisson regression models for discrete time series. Part 1: Methodology," Journal of Applied Statistics, Taylor & Francis Journals, vol. 26(7), pages 855-869.
    • Handle: RePEc:taf:japsta:v:26:y:1999:i:7:p:855-869
    DOI: 10.1080/02664769922098
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    References listed on IDEAS

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    1. Wang, Peiming & Cockburn, Iain M & Puterman, Martin L, 1998. "Analysis of Patent Data--A Mixed-Poisson-Regression-Model Approach," Journal of Business & Economic Statistics, American Statistical Association, vol. 16(1), pages 27-41, January.
    2. Peiming Wang & Martin Puterman, 1999. "Markov Poisson regression models for discrete time series. Part 2: Applications," Journal of Applied Statistics, Taylor & Francis Journals, vol. 26(7), pages 871-882.
    3. Ludwig Fahrmeir & Heinz Kaufmann, 1987. "Regression Models For Non‐Stationary Categorical Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 8(2), pages 147-160, March.
    4. Leroux, Brian G., 1992. "Maximum-likelihood estimation for hidden Markov models," Stochastic Processes and their Applications, Elsevier, vol. 40(1), pages 127-143, February.
    5. Peiming Wang & Iain Cockburn & Martin L. Puterman, "undated". "A Mixed Poisson Regression Model for Analysis of Patent Data," Computing in Economics and Finance 1996 _049, Society for Computational Economics.
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    Cited by:

    1. Pami Dua & Divya Tuteja, 2021. "Regime Shifts in the Behaviour of International Currency and Equity Markets: A Markov-Switching Analysis," Journal of Quantitative Economics, Springer;The Indian Econometric Society (TIES), vol. 19(1), pages 309-336, December.
    2. Peiming Wang & Martin Puterman, 1999. "Markov Poisson regression models for discrete time series. Part 2: Applications," Journal of Applied Statistics, Taylor & Francis Journals, vol. 26(7), pages 871-882.
    3. Park, Jeong-gun & Basawa, I. V., 2002. "Estimation for mixtures of Markov processes," Statistics & Probability Letters, Elsevier, vol. 59(3), pages 235-244, October.
    4. Dannemann, Jörn & Holzmann, Hajo, 2010. "Testing for two components in a switching regression model," Computational Statistics & Data Analysis, Elsevier, vol. 54(6), pages 1592-1604, June.

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