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Strict stationarity of Poisson integer-valued ARCH processes of order infinity

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  • Mawuli Segnon

Abstract

This paper establishes necessary and sufficient conditions for the existence of a unique strictly stationary and ergodic solution for integer-valued autoregressive conditional heteroscedasticity (INARCH) processes. We also provide conditions that guarantee existence of higher order moments. The results apply to integer-valued GARCH model, and its long-memory versions with hyperbolically decaying coefficients.

Suggested Citation

  • Mawuli Segnon, 2022. "Strict stationarity of Poisson integer-valued ARCH processes of order infinity," CQE Working Papers 10222, Center for Quantitative Economics (CQE), University of Muenster.
    • Handle: RePEc:cqe:wpaper:10222
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    File URL: https://www.wiwi.uni-muenster.de/cqe/sites/cqe/files/CQE_Paper/cqe_wp_102_2022.pdf
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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. Mawuli Segnon & Manuel Stapper, 2019. "Long Memory Conditional Heteroscedasticity in Count Data," CQE Working Papers 8219, Center for Quantitative Economics (CQE), University of Muenster.
    3. Doukhan, Paul & Wintenberger, Olivier, 2008. "Weakly dependent chains with infinite memory," Stochastic Processes and their Applications, Elsevier, vol. 118(11), pages 1997-2013, November.
    4. 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.
    5. Bougerol, Philippe & Picard, Nico, 1992. "Stationarity of Garch processes and of some nonnegative time series," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 115-127.
    6. Alain Latour, 1998. "Existence and Stochastic Structure of a Non‐negative Integer‐valued Autoregressive Process," Journal of Time Series Analysis, Wiley Blackwell, vol. 19(4), pages 439-455, July.
    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. Shiqing Ling & Michael McAleer, 2010. "A general asymptotic theory for time‐series models," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 64(1), pages 97-111, February.
    9. 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.
    10. Kazakevičius, Vytautas & Leipus, Remigijus, 2002. "On Stationarity In The Arch(∞) Model," Econometric Theory, Cambridge University Press, vol. 18(1), pages 1-16, February.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    INARCH processes; Stationarity; Ergodicity; Lyapunov exponent;
    All these keywords.

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
    • C4 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics
    • C5 - Mathematical and Quantitative Methods - - Econometric Modeling

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