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A note on the stability of multivariate non-linear time series with an application to time series of counts

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  • Debaly, Zinsou Max
  • Truquet, Lionel

Abstract

We introduce a simple criterion for studying stationarity and moments properties of some multivariate Markovian autoregressive processes, under a contracting mapping assumption. We apply our results to the Poisson INGARCH model and to one of its multivariate extension recently introduced in the literature. In particular, we obtain optimal stationarity conditions and existence of some exponential moments.

Suggested Citation

  • Debaly, Zinsou Max & Truquet, Lionel, 2021. "A note on the stability of multivariate non-linear time series with an application to time series of counts," Statistics & Probability Letters, Elsevier, vol. 179(C).
    • Handle: RePEc:eee:stapro:v:179:y:2021:i:c:s0167715221001589
    DOI: 10.1016/j.spl.2021.109196
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    References listed on IDEAS

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    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. 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.
    3. Yan Cui & Qi Li & Fukang Zhu, 2020. "Flexible bivariate Poisson integer-valued GARCH model," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 72(6), pages 1449-1477, December.
    4. 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.
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    Cited by:

    1. Debaly, Zinsou Max & Marchand, Philippe & Girona, Miguel Montoro, 2022. "Autoregressive models for time series of random sums of positive variables: Application to tree growth as a function of climate and insect outbreak," Ecological Modelling, Elsevier, vol. 471(C).
    2. Fokianos, Konstantinos, 2024. "Multivariate Count Time Series Modelling," Econometrics and Statistics, Elsevier, vol. 31(C), pages 100-116.
    3. Mirko Armillotta & Paolo Gorgi, 2023. "Pseudo-variance quasi-maximum likelihood estimation of semi-parametric time series models," Tinbergen Institute Discussion Papers 23-054/III, Tinbergen Institute.
    4. Truquet, Lionel, 2023. "Strong mixing properties of discrete-valued time series with exogenous covariates," Stochastic Processes and their Applications, Elsevier, vol. 160(C), pages 294-317.

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