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Portmanteau tests for ARMA models with infinite variance

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  • J.-W. Lin
  • A. I. McLeod

Abstract

Autoregressive and moving-average (ARMA) models with stable Paretian errors are some of the most studied models for time series with infinite variance. Estimation methods for these models have been studied by many researchers but the problem of diagnostic checking of fitted models has not been addressed. In this article, we develop portmanteau tests for checking the randomness of a time series with infinite variance and for ARMA diagnostic checking when the innovations have infinite variance. It is assumed that least squares or an asymptotically equivalent estimation method, such as Gaussian maximum likelihood, is used. It is also assumed that the distribution of the innovations is identically and independently distributed (i.i.d.) stable Paretian. It is seen via simulation that the proposed portmanteau tests do not converge well to the corresponding limiting distributions for practical series length so a Monte Carlo test is suggested. Simulation experiments show that the proposed Monte Carlo test procedure works effectively. Two illustrative applications to actual data are provided to demonstrate that an incorrect conclusion may result if the usual portmanteau test based on the finite variance assumption is used. Copyright 2008 The Authors

Suggested Citation

  • J.-W. Lin & A. I. McLeod, 2008. "Portmanteau tests for ARMA models with infinite variance," Journal of Time Series Analysis, Wiley Blackwell, vol. 29(3), pages 600-617, May.
  • Handle: RePEc:bla:jtsera:v:29:y:2008:i:3:p:600-617
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    Cited by:

    1. Serttas, Fatma Ozgu, 2010. "Essays on infinite-variance stable errors and robust estimation procedures," ISU General Staff Papers 201001010800002742, Iowa State University, Department of Economics.
    2. Lee, Sangyeol & Tim Ng, Chi, 2010. "Trimmed portmanteau test for linear processes with infinite variance," Journal of Multivariate Analysis, Elsevier, vol. 101(4), pages 984-998, April.
    3. Bouhaddioui, Chafik & Ghoudi, Kilani, 2012. "Empirical processes for infinite variance autoregressive models," Journal of Multivariate Analysis, Elsevier, vol. 107(C), pages 319-335.
    4. Fries, Sébastien & Zakoian, Jean-Michel, 2017. "Mixed Causal-Noncausal AR Processes and the Modelling of Explosive Bubbles," MPRA Paper 81345, University Library of Munich, Germany.
    5. Marc S. Paolella, 2016. "Stable-GARCH Models for Financial Returns: Fast Estimation and Tests for Stability," Econometrics, MDPI, Open Access Journal, vol. 4(2), pages 1-28, May.
    6. Christian Gouriéroux & Jean-Michel Zakoïan, 2017. "Local explosion modelling by non-causal process," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 79(3), pages 737-756, June.
    7. repec:gam:jecnmx:v:4:y:2016:i:2:p:25:d:69492 is not listed on IDEAS

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