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Ergodicity conditions for a double mixed Poisson autoregression

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  • Aknouche, Abdelhakim
  • Demmouche, Nacer

Abstract

We propose a double mixed Poisson autoregression in which the intensity, scaled by a unit mean independent and identically distributed (i.i.d.) mixing process, has different regime specifications according to the state of a finite unobserved i.i.d. 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.

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  • Aknouche, Abdelhakim & Demmouche, Nacer, 2019. "Ergodicity conditions for a double mixed Poisson autoregression," Statistics & Probability Letters, Elsevier, vol. 147(C), pages 6-11.
    • Handle: RePEc:eee:stapro:v:147:y:2019:i:c:p:6-11
    DOI: 10.1016/j.spl.2018.11.030
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    References listed on IDEAS

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    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. 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.
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    4. Doukhan, Paul & Wintenberger, Olivier, 2008. "Weakly dependent chains with infinite memory," Stochastic Processes and their Applications, Elsevier, vol. 118(11), pages 1997-2013, November.
    5. 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.
    6. 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.
    7. Doukhan, Paul & Fokianos, Konstantinos & Tjøstheim, Dag, 2012. "On weak dependence conditions for Poisson autoregressions," Statistics & Probability Letters, Elsevier, vol. 82(5), pages 942-948.
    8. Fukang Zhu, 2011. "A negative binomial integer‐valued GARCH model," Journal of Time Series Analysis, Wiley Blackwell, vol. 32(1), pages 54-67, January.
    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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    Cited by:

    1. Abdelhakim Aknouche & Christian Francq, 2022. "Stationarity and ergodicity of Markov switching positive conditional mean models," Journal of Time Series Analysis, Wiley Blackwell, vol. 43(3), pages 436-459, May.
    2. Aknouche, Abdelhakim & Dimitrakopoulos, Stefanos & Touche, Nassim, 2019. "Integer-valued stochastic volatility," MPRA Paper 91962, University Library of Munich, Germany, revised 04 Feb 2019.
    3. Aknouche, Abdelhakim & Dimitrakopoulos, Stefanos, 2020. "On an integer-valued stochastic intensity model for time series of counts," MPRA Paper 105406, University Library of Munich, Germany.
    4. Aknouche, Abdelhakim, 2024. "Periodically homogeneous Markov chains: The discrete state space case," MPRA Paper 122287, University Library of Munich, Germany.
    5. Aknouche, Abdelhakim & Dimitrakopoulos, Stefanos, 2024. "Volatility models versus intensity models: analogy and differences," MPRA Paper 122528, University Library of Munich, Germany.

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