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On uniqueness of moving average representations of heavy-tailed stationary processes

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  • Gouriéroux, Christian
  • Zakoian, Jean-Michel

Abstract

We prove the uniqueness of linear i.i.d. representations of heavy-tailed processes whose distribution belongs to the domain of attraction of an $\alpha$-stable law, with $\alpha

Suggested Citation

  • Gouriéroux, Christian & Zakoian, Jean-Michel, 2014. "On uniqueness of moving average representations of heavy-tailed stationary processes," MPRA Paper 54907, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:54907
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    File URL: https://mpra.ub.uni-muenchen.de/54907/1/MPRA_paper_54907.pdf
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    References listed on IDEAS

    as
    1. Christian Gouriéroux & Jean-Michel Zakoian, 2013. "Explosive Bubble Modelling by Noncausal Process," Working Papers 2013-04, Center for Research in Economics and Statistics.
    2. Marc Hallin & Claude Lefèvre & Madan Lal Puri, 1988. "On time-reversibility and the uniqueness of moving average representations for non-Gaussian stationary time series," ULB Institutional Repository 2013/2017, ULB -- Universite Libre de Bruxelles.
    3. Kung-Sik Chan & Lop-Hing Ho & Howell Tong, 2006. "A note on time-reversibility of multivariate linear processes," Biometrika, Biometrika Trust, vol. 93(1), pages 221-227, March.
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    Cited by:

    1. Christian Gourieroux & Andrew Hencic & Joann Jasiak, 2021. "Forecast performance and bubble analysis in noncausal MAR(1, 1) processes," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 40(2), pages 301-326, March.
    2. Fries, Sébastien & Zakoian, Jean-Michel, 2019. "Mixed Causal-Noncausal Ar Processes And The Modelling Of Explosive Bubbles," Econometric Theory, Cambridge University Press, vol. 35(6), pages 1234-1270, December.
    3. Frédérique Bec & Heino Bohn Nielsen & Sarra Saïdi, 2020. "Mixed Causal–Noncausal Autoregressions: Bimodality Issues in Estimation and Unit Root Testing," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 82(6), pages 1413-1428, December.
    4. Gourieroux, Christian & Jasiak, Joann, 2018. "Misspecification of noncausal order in autoregressive processes," Journal of Econometrics, Elsevier, vol. 205(1), pages 226-248.

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    More about this item

    Keywords

    $alpha$-stable distribution; Domain of attraction; Infinite moving average; Linear process; Mixed causal/noncausal process; Nonparametric identification; Unobserved component model.;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models

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