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On Uniqueness of Moving Average Representations of Heavy-tailed Stationary Processes

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  • Christian Gouriéroux
  • Jean-Michel Zakoïan

Abstract

type="main" xml:id="jtsa12139-abs-0001"> The paper solves the open problem of identification of two-sided moving average representations with i.i.d. summands, for stationary processes in non-Gaussian domains of attraction of α-stable laws. This shows the possibility to identify nonparametrically both the sequence of two-sided moving average coefficients and the distribution of the underlying heavy-tailed i.i.d. process.

Suggested Citation

  • Christian Gouriéroux & Jean-Michel Zakoïan, 2015. "On Uniqueness of Moving Average Representations of Heavy-tailed Stationary Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 36(6), pages 876-887, November.
    • Handle: RePEc:bla:jtsera:v:36:y:2015:i:6:p:876-887
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    File URL: http://hdl.handle.net/10.1111/jtsa.12139
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    References listed on IDEAS

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    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. 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.
    2. 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.
    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

    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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