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Sign-based portmanteau test for ARCH-type models with heavy-tailed innovations

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  • Chen, Min
  • Zhu, Ke

Abstract

This paper proposes a sign-based portmanteau test for diagnostic checking of ARCH-type models estimated by the least absolute deviation approach. Under the strict stationarity condition, the asymptotic distribution is obtained. The new test is applicable for very heavy-tailed innovations with only finite fractional moments. Simulations are undertaken to assess the performance of the sign-based test, as well as a comparison with other two portmanteau tests. A real empirical example for exchange rates is given to illustrate the practical usefulness of the test.

Suggested Citation

  • Chen, Min & Zhu, Ke, 2013. "Sign-based portmanteau test for ARCH-type models with heavy-tailed innovations," MPRA Paper 50487, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:50487
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    File URL: https://mpra.ub.uni-muenchen.de/50487/1/MPRA_paper_50487.pdf
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    References listed on IDEAS

    as
    1. Ling, Shiqing & McAleer, Michael, 2003. "Asymptotic Theory For A Vector Arma-Garch Model," Econometric Theory, Cambridge University Press, vol. 19(02), pages 280-310, April.
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    3. Jianqing Fan & Lei Qi & Dacheng Xiu, 2014. "Quasi-Maximum Likelihood Estimation of GARCH Models With Heavy-Tailed Likelihoods," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 32(2), pages 178-191, April.
    4. Linton, Oliver & Pan, Jiazhu & Wang, Hui, 2010. "Estimation For A Nonstationary Semi-Strong Garch(1,1) Model With Heavy-Tailed Errors," Econometric Theory, Cambridge University Press, vol. 26(01), pages 1-28, February.
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    9. Francq, Christian & Wintenberger, Olivier & Zakoïan, Jean-Michel, 2013. "GARCH models without positivity constraints: Exponential or log GARCH?," Journal of Econometrics, Elsevier, vol. 177(1), pages 34-46.
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    11. Hall, Peter & Yao, Qiwei, 2003. "Inference in ARCH and GARCH models with heavy-tailed errors," LSE Research Online Documents on Economics 5875, London School of Economics and Political Science, LSE Library.
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    Citations

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    Cited by:

    1. Ling, Shiqing & McAleer, Michael & Tong, Howell, 2015. "Frontiers in Time Series and Financial Econometrics: An overview," Journal of Econometrics, Elsevier, vol. 189(2), pages 245-250.
    2. Li, Dong & Ling, Shiqing & Zhu, Ke, 2016. "ZD-GARCH model: a new way to study heteroscedasticity," MPRA Paper 68621, University Library of Munich, Germany.
    3. Ke Zhu, 2016. "Bootstrapping the portmanteau tests in weak auto-regressive moving average models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 78(2), pages 463-485, March.
    4. Zhu, Ke, 2015. "Hausman tests for the error distribution in conditionally heteroskedastic models," MPRA Paper 66991, University Library of Munich, Germany.
    5. Ling, S. & McAleer, M.J. & Tong, H., 2015. "Frontiers in Time Series and Financial Econometrics," Econometric Institute Research Papers EI 2015-07, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    6. repec:eee:econom:v:202:y:2018:i:1:p:1-17 is not listed on IDEAS

    More about this item

    Keywords

    ARCH-type model; heavy-tailed innovation; LAD estimator; model diagnostics; sign-based portmanteau test;

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General

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