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Least absolute deviation estimation for fractionally integrated autoregressive moving average time series models with conditional heteroscedasticity

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  • Guodong Li
  • Wai Keung Li

Abstract

We consider a unified least absolute deviation estimator for stationary and nonstationary fractionally integrated autoregressive moving average models with conditional heteroscedasticity. Its asymptotic normality is established when the second moments of errors and innovations are finite. Several other alternative estimators are also discussed and are shown to be less efficient and less robust than the proposed approach. A diagnostic tool, consisting of two portmanteau tests, is designed to check whether or not the estimated models are adequate. The simulation experiments give further support to our model and the results for the absolute returns of the Dow Jones Industrial Average Index daily closing price demonstrate their usefulness in modelling time series exhibiting the features of long memory, conditional heteroscedasticity and heavy tails. Copyright 2008, Oxford University Press.

Suggested Citation

  • Guodong Li & Wai Keung Li, 2008. "Least absolute deviation estimation for fractionally integrated autoregressive moving average time series models with conditional heteroscedasticity," Biometrika, Biometrika Trust, vol. 95(2), pages 399-414.
    • Handle: RePEc:oup:biomet:v:95:y:2008:i:2:p:399-414
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    File URL: http://hdl.handle.net/10.1093/biomet/asn014
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    Citations

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    Cited by:

    1. Uwe Hassler & Paulo M.M. Rodrigues & Antonio Rubia, 2016. "Quantile Regression for Long Memory Testing: A Case of Realized Volatility," Journal of Financial Econometrics, Oxford University Press, vol. 14(4), pages 693-724.
    2. 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.
    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. Paulo M.M. Rodrigues & Matei Demetrescu, 2018. "Testing the fractionally integrated hypothesis using M estimation: With an application to stock market volatility," Working Papers w201817, Banco de Portugal, Economics and Research Department.
    5. Ke Zhu & Shiqing Ling, 2015. "LADE-Based Inference for ARMA Models With Unspecified and Heavy-Tailed Heteroscedastic Noises," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(510), pages 784-794, June.
    6. 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.
    7. 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.
    8. Zhang, Xingfa & Zhang, Rongmao & Li, Yuan & Ling, Shiqing, 2022. "LADE-based inferences for autoregressive models with heavy-tailed G-GARCH(1, 1) noise," Journal of Econometrics, Elsevier, vol. 227(1), pages 228-240.
    9. 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.
    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. Zhu, Ke & Li, Wai Keung, 2013. "A new Pearson-type QMLE for conditionally heteroskedastic models," MPRA Paper 52344, University Library of Munich, Germany.
    12. 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.
    13. Guodong Li & Chenlei Leng & Chih-Ling Tsai, 2014. "A Hybrid Bootstrap Approach To Unit Root Tests," Journal of Time Series Analysis, Wiley Blackwell, vol. 35(4), pages 299-321, July.
    14. 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.
    15. 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.
    16. Zhu, Qianqian & Zheng, Yao & Li, Guodong, 2018. "Linear double autoregression," Journal of Econometrics, Elsevier, vol. 207(1), pages 162-174.

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