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On weak dependence conditions for Poisson autoregressions

Author

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  • Doukhan, Paul
  • Fokianos, Konstantinos
  • Tjøstheim, Dag

Abstract

We consider generalized linear models for regression modeling of count time series. We give easily verifiable conditions for obtaining weak dependence for such models. These results enable the development of maximum likelihood inference under minimal conditions. Some examples which are useful to applications are discussed in detail.

Suggested Citation

  • Doukhan, Paul & Fokianos, Konstantinos & Tjøstheim, Dag, 2012. "On weak dependence conditions for Poisson autoregressions," Statistics & Probability Letters, Elsevier, vol. 82(5), pages 942-948.
  • Handle: RePEc:eee:stapro:v:82:y:2012:i:5:p:942-948
    DOI: 10.1016/j.spl.2012.01.015
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    References listed on IDEAS

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    1. Fokianos, Konstantinos & Rahbek, Anders & Tjøstheim, Dag, 2009. "Poisson Autoregression," Journal of the American Statistical Association, American Statistical Association, vol. 104(488), pages 1430-1439.
    2. Richard A. Davis, 2003. "Observation-driven models for Poisson counts," Biometrika, Biometrika Trust, vol. 90(4), pages 777-790, December.
    3. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    4. Doukhan, Paul & Louhichi, Sana, 1999. "A new weak dependence condition and applications to moment inequalities," Stochastic Processes and their Applications, Elsevier, vol. 84(2), pages 313-342, December.
    5. Doukhan, Paul & Wintenberger, Olivier, 2008. "Weakly dependent chains with infinite memory," Stochastic Processes and their Applications, Elsevier, vol. 118(11), pages 1997-2013, November.
    6. René Ferland & Alain Latour & Driss Oraichi, 2006. "Integer‐Valued GARCH Process," Journal of Time Series Analysis, Wiley Blackwell, vol. 27(6), pages 923-942, November.
    7. Fokianos, Konstantinos & Tjøstheim, Dag, 2011. "Log-linear Poisson autoregression," Journal of Multivariate Analysis, Elsevier, vol. 102(3), pages 563-578, March.
    8. Konstantinos Fokianos & Dag Tjøstheim, 2012. "Nonlinear Poisson autoregression," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 64(6), pages 1205-1225, December.
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