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Ergodicity conditions for a double mixed Poisson autoregression

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  • Aknouche, Abdelhakim
  • Demouche, Nacer

Abstract

We propose a double mixed Poisson autoregression in which the intensity, scaled by a unit mean independent and identically distributed (iid) mixing process, has different regime specifications according to the state of a finite unobserved iid chain. Under some contraction in mean conditions, we show that the proposed model is strictly stationary and ergodic with a finite mean. Applications to various count time series models are given.

Suggested Citation

  • Aknouche, Abdelhakim & Demouche, Nacer, 2018. "Ergodicity conditions for a double mixed Poisson autoregression," MPRA Paper 88843, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:88843
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    References listed on IDEAS

    as
    1. Luc Bauwens & Arie Preminger & Jeroen V. K. Rombouts, 2010. "Theory and inference for a Markov switching GARCH model," Econometrics Journal, Royal Economic Society, vol. 13(2), pages 218-244, July.
    2. Markus Haas, 2004. "A New Approach to Markov-Switching GARCH Models," Journal of Financial Econometrics, Oxford University Press, vol. 2(4), pages 493-530.
    3. Aknouche, Abdelhakim & Bentarzi, Wissam & Demouche, Nacer, 2018. "On periodic ergodicity of a general periodic mixed Poisson autoregression," Statistics & Probability Letters, Elsevier, vol. 134(C), pages 15-21.
    4. Doukhan, Paul & Fokianos, Konstantinos & Tjøstheim, Dag, 2012. "On weak dependence conditions for Poisson autoregressions," Statistics & Probability Letters, Elsevier, vol. 82(5), pages 942-948.
    5. Fukang Zhu, 2011. "A negative binomial integer‐valued GARCH model," Journal of Time Series Analysis, Wiley Blackwell, vol. 32(1), pages 54-67, January.
    6. 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.
    7. Doukhan, Paul & Wintenberger, Olivier, 2008. "Weakly dependent chains with infinite memory," Stochastic Processes and their Applications, Elsevier, vol. 118(11), pages 1997-2013, November.
    8. Abdelhakim Aknouche & Nadia Rabehi, 2010. "On an independent and identically distributed mixture bilinear time‐series model," Journal of Time Series Analysis, Wiley Blackwell, vol. 31(2), pages 113-131, March.
    9. Francq, Christian & ZakoI¨an, Jean-Michel, 2008. "Deriving the autocovariances of powers of Markov-switching GARCH models, with applications to statistical inference," Computational Statistics & Data Analysis, Elsevier, vol. 52(6), pages 3027-3046, February.
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    More about this item

    Keywords

    Double mixed Poisson autoregression; negative binomial mixture INGARCH model; ergodicity; weak dependence; contraction in mean;
    All these keywords.

    JEL classification:

    • C40 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - General
    • C46 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Specific Distributions
    • C50 - Mathematical and Quantitative Methods - - Econometric Modeling - - - General

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