IDEAS home Printed from https://ideas.repec.org/p/cqe/wpaper/10222.html
   My bibliography  Save this paper

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: https://www.wiwi.uni-muenster.de/cqe/sites/cqe/files/CQE_Paper/cqe_wp_102_2022.pdf
    File Function: Version of May 2023
    Download Restriction: no
    ---><---

    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)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Huiyu Mao & Fukang Zhu & Yan Cui, 2020. "A generalized mixture integer-valued GARCH model," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 29(3), pages 527-552, September.
    2. William Kengne & Isidore S. Ngongo, 2022. "Inference for nonstationary time series of counts with application to change-point problems," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 74(4), pages 801-835, August.
    3. 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.
    4. Moysiadis, Theodoros & Fokianos, Konstantinos, 2014. "On binary and categorical time series models with feedback," Journal of Multivariate Analysis, Elsevier, vol. 131(C), pages 209-228.
    5. Cui, Yunwei & Zheng, Qi, 2017. "Conditional maximum likelihood estimation for a class of observation-driven time series models for count data," Statistics & Probability Letters, Elsevier, vol. 123(C), pages 193-201.
    6. Weiß, Christian H. & Zhu, Fukang, 2024. "Conditional-mean multiplicative operator models for count time series," Computational Statistics & Data Analysis, Elsevier, vol. 191(C).
    7. 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.
    8. Mengya Liu & Qi Li & Fukang Zhu, 2020. "Self-excited hysteretic negative binomial autoregression," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 104(3), pages 385-415, September.
    9. Mamadou Lamine Diop & William Kengne, 2017. "Testing Parameter Change in General Integer-Valued Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 38(6), pages 880-894, November.
    10. Doukhan, Paul & Fokianos, Konstantinos & Tjøstheim, Dag, 2012. "On weak dependence conditions for Poisson autoregressions," Statistics & Probability Letters, Elsevier, vol. 82(5), pages 942-948.
    11. Yan Cui & Fukang Zhu, 2018. "A new bivariate integer-valued GARCH model allowing for negative cross-correlation," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 27(2), pages 428-452, June.
    12. Jiwon Kang & Sangyeol Lee, 2014. "Parameter Change Test for Poisson Autoregressive Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 41(4), pages 1136-1152, December.
    13. Aknouche, Abdelhakim & Bendjeddou, Sara, 2016. "Negative binomial quasi-likelihood inference for general integer-valued time series models," MPRA Paper 76574, University Library of Munich, Germany, revised 03 Feb 2017.
    14. Fokianos, Konstantinos & Moysiadis, Theodoros, 2017. "Binary time series models driven by a latent process," Econometrics and Statistics, Elsevier, vol. 2(C), pages 117-130.
    15. 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.
    16. 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.
    17. Hanan Elsaied & Roland Fried, 2014. "Robust Fitting Of Inarch Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 35(6), pages 517-535, November.
    18. Xinyang Wang & Dehui Wang & Kai Yang, 2021. "Integer-valued time series model order shrinkage and selection via penalized quasi-likelihood approach," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 84(5), pages 713-750, July.
    19. 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.
    20. 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.

    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

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:cqe:wpaper:10222. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Susanne Deckwitz (email available below). General contact details of provider: https://edirc.repec.org/data/cqmuede.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.