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A Linear Poisson Autoregressive Model: The Poisson AR(p) Model

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  • Brandt, Patrick T.
  • Williams, John T.

Abstract

Time series of event counts are common in political science and other social science applications. Presently, there are few satisfactory methods for identifying the dynamics in such data and accounting for the dynamic processes in event counts regression. We address this issue by building on earlier work for persistent event counts in the Poisson exponentially weighted moving-average model (PEWMA) of Brandt et al. (American Journal of Political Science 44(4):823–843, 2000). We develop an alternative model for stationary mean reverting data, the Poisson autoregressive model of order p, or PAR(p) model. Issues of identification and model selection are also considered. We then evaluate the properties of this model and present both Monte Carlo evidence and applications to illustrate.

Suggested Citation

  • Brandt, Patrick T. & Williams, John T., 2001. "A Linear Poisson Autoregressive Model: The Poisson AR(p) Model," Political Analysis, Cambridge University Press, vol. 9(2), pages 164-184, January.
    • Handle: RePEc:cup:polals:v:9:y:2001:i:02:p:164-184_00
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    10. Worrall, John L. & Gaines, Larry K., 2006. "The effect of police-probation partnerships on juvenile arrests," Journal of Criminal Justice, Elsevier, vol. 34(6), pages 579-589.
    11. Braun, Robert & Koopmans, Ruud, 2014. "Watch the Crowd: Bystander Responses, Trickle-Down Politics, and Xenophobic Mobilization," EconStor Open Access Articles and Book Chapters, ZBW - Leibniz Information Centre for Economics, vol. 47(4), pages 631-658.
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    14. Benjamin O. Fordham, 2004. "A Very Sharp Sword," Journal of Conflict Resolution, Peace Science Society (International), vol. 48(5), pages 632-656, October.
    15. Brandt, Patrick T. & Sandler, Todd, 2009. "Hostage taking: Understanding terrorism event dynamics," Journal of Policy Modeling, Elsevier, vol. 31(5), pages 758-778, September.
    16. Tom S. Clark, 2009. "The Separation of Powers, Court Curbing, and Judicial Legitimacy," American Journal of Political Science, John Wiley & Sons, vol. 53(4), pages 971-989, October.
    17. Worrall, John L. & Hiromoto, Scott & Merritt, Nancy & Du, Dan & Jacobson, Jerry O. & Iguchi, Martin Y., 2009. "Crime trends and the effect of mandated drug treatment: Evidence from California's Substance Abuse and Crime Prevention Act," Journal of Criminal Justice, Elsevier, vol. 37(2), pages 109-113, March.
    18. Braun, Robert & Koopmans, Ruud, 2012. "Bystander responses and xenophobic mobilization," Discussion Papers, Research Unit: Migration, Integration, Transnationalization SP IV 2012-701, WZB Berlin Social Science Center.
    19. Mailu, Stephen & Lukibisi, Barasa & Waithaka, Michael, 2011. "Application of various count models: Sahiwal demand from Naivasha," MPRA Paper 32074, University Library of Munich, Germany, revised 06 Jul 2011.

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