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On periodic ergodicity of a general periodic mixed Poisson autoregression

Author

Listed:
  • Aknouche, Abdelhakim
  • Bentarzi, Wissam
  • Demouche, Nacer

Abstract

We propose a general class of non-linear mixed Poisson autoregressions whose form and parameters are periodic over time. Under a periodic contraction condition on the forms of the conditional mean, we show the existence of a unique nonanticipative solution to the model, which is strictly periodically stationary, periodically ergodic and periodically weakly dependent having in the pure Poisson case finite higher-order moments. Applications to some well-known integer-valued time series models are considered.

Suggested Citation

  • Aknouche, Abdelhakim & Bentarzi, Wissam & Demouche, Nacer, 2017. "On periodic ergodicity of a general periodic mixed Poisson autoregression," MPRA Paper 79650, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:79650
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    References listed on IDEAS

    as
    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. Vasiliki Christou & Konstantinos Fokianos, 2014. "Quasi-Likelihood Inference For Negative Binomial Time Series Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 35(1), pages 55-78, January.
    3. Chao Wang & Heng Liu & Jian-Feng Yao & Richard A. Davis & Wai Keung Li, 2014. "Self-Excited Threshold Poisson Autoregression," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(506), pages 777-787, June.
    4. Ali Ahmad & Christian Francq, 2016. "Poisson QMLE of Count Time Series Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 37(3), pages 291-314, May.
    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. Douc, R. & Doukhan, P. & Moulines, E., 2013. "Ergodicity of observation-driven time series models and consistency of the maximum likelihood estimator," Stochastic Processes and their Applications, Elsevier, vol. 123(7), pages 2620-2647.
    7. Fokianos, Konstantinos & Tjøstheim, Dag, 2011. "Log-linear Poisson autoregression," Journal of Multivariate Analysis, Elsevier, vol. 102(3), pages 563-578, March.
    8. Doukhan, Paul & Fokianos, Konstantinos & Tjøstheim, Dag, 2012. "On weak dependence conditions for Poisson autoregressions," Statistics & Probability Letters, Elsevier, vol. 82(5), pages 942-948.
    9. Tina Hviid Rydberg & Neil Shephard, 2000. "BIN Models for Trade-by-Trade Data. Modelling the Number of Trades in a Fixed Interval of Time," Econometric Society World Congress 2000 Contributed Papers 0740, Econometric Society.
    10. 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.
    11. Fukang Zhu, 2011. "A negative binomial integer‐valued GARCH model," Journal of Time Series Analysis, Wiley Blackwell, vol. 32(1), pages 54-67, January.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Periodic mixed Poisson autoregression; periodic INGARCH models; non-linear INGARCH models; weak dependence; strict periodic stationarity; periodic ergodicity; periodic contraction condition.;
    All these keywords.

    JEL classification:

    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
    • C19 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Other
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium

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