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Diagnostic checking for time series models with conditional heteroscedasticity estimated by the least absolute deviation approach

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  • Guodong Li
  • Wai Keung Li

Abstract

The recent paper by Peng & Yao (2003) gave an interesting extension of least absolute deviation estimation to generalised autoregressive conditional heteroscedasticity, GARCH, time series models. The asymptotic distributions of absolute residual autocorrelations and squared residual autocorrelations from the GARCH model estimated by the least absolute deviation method are derived in this paper. These results lead to two useful diagnostic tools which can be used to check whether or not a GARCH model fitted by using the least absolute deviation method is adequate. Some simulation experiments give further support to the asymptotic theory and a real data example is also reported. Copyright 2005, Oxford University Press.

Suggested Citation

  • Guodong Li & Wai Keung Li, 2005. "Diagnostic checking for time series models with conditional heteroscedasticity estimated by the least absolute deviation approach," Biometrika, Biometrika Trust, vol. 92(3), pages 691-701, September.
    • Handle: RePEc:oup:biomet:v:92:y:2005:i:3:p:691-701
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    Citations

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    Cited by:

    1. 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.
    2. Li, Muyi & Li, Wai Keung & Li, Guodong, 2015. "A new hyperbolic GARCH model," Journal of Econometrics, Elsevier, vol. 189(2), pages 428-436.
    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. Kwan, Wilson & Li, Wai Keung & Li, Guodong, 2012. "On the estimation and diagnostic checking of the ARFIMA–HYGARCH model," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3632-3644.
    5. Guodong Li & Qianqian Zhu & Zhao Liu & Wai Keung Li, 2017. "On Mixture Double Autoregressive Time Series Models," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 35(2), pages 306-317, April.
    6. De Gooijer, Jan G., 2023. "On portmanteau-type tests for nonlinear multivariate time series," Journal of Multivariate Analysis, Elsevier, vol. 195(C).
    7. Songhua Tan & Qianqian Zhu, 2022. "Asymmetric linear double autoregression," Journal of Time Series Analysis, Wiley Blackwell, vol. 43(3), pages 371-388, May.
    8. Chen, Min & Zhu, Ke, 2015. "Sign-based portmanteau test for ARCH-type models with heavy-tailed innovations," Journal of Econometrics, Elsevier, vol. 189(2), pages 313-320.
    9. Wang, Xuqin & Li, Muyi, 2023. "Bootstrapping the transformed goodness-of-fit test on heavy-tailed GARCH models," Computational Statistics & Data Analysis, Elsevier, vol. 184(C).
    10. Li, Dong & Ling, Shiqing & Zhu, Ke, 2016. "ZD-GARCH model: a new way to study heteroscedasticity," MPRA Paper 68621, University Library of Munich, Germany.
    11. Qiang Xia & Zhiqiang Zhang & Wai Keung Li, 2020. "A Portmanteau Test for Smooth Transition Autoregressive Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 41(5), pages 722-730, September.
    12. Yaxing Yang & Shiqing Ling, 2017. "Inference for Heavy-Tailed and Multiple-Threshold Double Autoregressive Models," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 35(2), pages 318-333, April.
    13. Philip L. H. Yu & Guodong Li, 2014. "Comment," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 32(2), pages 166-167, April.
    14. Zhu, Ke & Ling, Shiqing, 2013. "Global self-weighted and local quasi-maximum exponential likelihood estimators for ARMA-GARCH/IGARCH models," MPRA Paper 51509, University Library of Munich, Germany.
    15. Yang, Yaxing & Ling, Shiqing, 2017. "Self-weighted LAD-based inference for heavy-tailed threshold autoregressive models," Journal of Econometrics, Elsevier, vol. 197(2), pages 368-381.
    16. Zhu, Ke, 2012. "A mixed portmanteau test for ARMA-GARCH model by the quasi-maximum exponential likelihood estimation approach," MPRA Paper 40382, University Library of Munich, Germany.
    17. Li, Dong & Zhang, Xingfa & Zhu, Ke & Ling, Shiqing, 2018. "The ZD-GARCH model: A new way to study heteroscedasticity," Journal of Econometrics, Elsevier, vol. 202(1), pages 1-17.

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