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Bootstrapping the transformed goodness-of-fit test on heavy-tailed GARCH models

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  • Wang, Xuqin
  • Li, Muyi

Abstract

We study the bootstrap inference on the goodness-of-fit test for generalized autoregressive conditional heteroskedastic (GARCH) models. Note that the commonly-used portmanteau tests for model adequacy checking necessarily impose moment conditions on innovations, we hence construct the test on the sample autocorrelations of a bounded transformation of absolute residuals, which are obtained by the least absolute deviation estimation from a fitted GARCH model. Specifically, we employ the empirical distribution function of absolute residuals as the transformation. Thus the corresponding portmanteau tests are applicable for very heavy-tailed innovations with only finite fractional moments. We bootstrap both the estimation equation and sample autocorrelations of transformed residuals to approximate the test statistics. The asymptotic validity of the bootstrap procedure is established. Monte Carlo experiments compare the finite-sample performance of the proposed bootstrap-based test with other existing tests. An empirical analysis of modeling exchange rates illustrates its usefulness.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:csdana:v:184:y:2023:i:c:s0167947323000555
    DOI: 10.1016/j.csda.2023.107744
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    as
    1. Roger Koenker, 2017. "Quantile Regression: 40 Years On," Annual Review of Economics, Annual Reviews, vol. 9(1), pages 155-176, September.
    2. Li, Muyi & Zhang, Yanfen, 2022. "Bootstrapping multivariate portmanteau tests for vector autoregressive models with weak assumptions on errors," Computational Statistics & Data Analysis, Elsevier, vol. 165(C).
    3. Yao Zheng & Wai Keung Li & Guodong Li, 2018. "A robust goodness-of-fit test for generalized autoregressive conditional heteroscedastic models," Biometrika, Biometrika Trust, vol. 105(1), pages 73-89.
    4. Yao Zheng & Qianqian Zhu & Guodong Li & Zhijie Xiao, 2018. "Hybrid quantile regression estimation for time series models with conditional heteroscedasticity," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 80(5), pages 975-993, November.
    5. 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.
    6. 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.
    7. Dufour, Jean-Marie & Roy, Roch, 1985. "Some robust exact results on sample autocorrelations and tests of randomness," Journal of Econometrics, Elsevier, vol. 29(3), pages 257-273, September.
    8. 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.
    9. Guo, Shaojun & Li, Dong & Li, Muyi, 2019. "Strict stationarity testing and GLAD estimation of double autoregressive models," Journal of Econometrics, Elsevier, vol. 211(2), pages 319-337.
    10. Jeong, Minsoo, 2017. "Residual-Based Garch Bootstrap And Second Order Asymptotic Refinement," Econometric Theory, Cambridge University Press, vol. 33(3), pages 779-790, June.
    11. Roger Koenker, 2017. "Quantile regression 40 years on," CeMMAP working papers CWP36/17, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    12. 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.
    13. Michele Leonardo Bianchi & Stoyan V Stoyanov & Gian Luca Tassinari & Frank J Fabozzi & Sergio M Focardi, 2019. "Handbook of Heavy-Tailed Distributions in Asset Management and Risk Management," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 11118, August.
    14. Liang Peng, 2003. "Least absolute deviations estimation for ARCH and GARCH models," Biometrika, Biometrika Trust, vol. 90(4), pages 967-975, December.
    15. Peng, Liang & Yao, Qiwei, 2003. "Least absolute deviations estimation for ARCH and GARCH models," LSE Research Online Documents on Economics 5828, London School of Economics and Political Science, LSE Library.
    16. Wan, Phyllis & Davis, Richard A., 2022. "Goodness-of-fit testing for time series models via distance covariance," Journal of Econometrics, Elsevier, vol. 227(1), pages 4-24.
    17. Zhu, Ke & Li, Wai Keung, 2015. "A bootstrapped spectral test for adequacy in weak ARMA models," Journal of Econometrics, Elsevier, vol. 187(1), pages 113-130.
    18. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    19. Giuseppe Cavaliere & Rasmus Søndergaard Pedersen & Anders Rahbek, 2018. "The Fixed Volatility Bootstrap for a Class of Arch(q) Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 39(6), pages 920-941, November.
    20. 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.
    21. Carlos Escanciano, J., 2008. "Joint and marginal specification tests for conditional mean and variance models," Journal of Econometrics, Elsevier, vol. 143(1), pages 74-87, March.
    22. Bougerol, Philippe & Picard, Nico, 1992. "Stationarity of Garch processes and of some nonnegative time series," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 115-127.
    23. K Mukherjee, 2020. "Bootstrapping M-estimators in generalized autoregressive conditional heteroscedastic models," Biometrika, Biometrika Trust, vol. 107(3), pages 753-760.
    24. Shao, Xiaofeng, 2011. "A bootstrap-assisted spectral test of white noise under unknown dependence," Journal of Econometrics, Elsevier, vol. 162(2), pages 213-224, June.
    25. R. Cont, 2001. "Empirical properties of asset returns: stylized facts and statistical issues," Quantitative Finance, Taylor & Francis Journals, vol. 1(2), pages 223-236.
    26. Qianqian Zhu & Ruochen Zeng & Guodong Li, 2020. "Bootstrap Inference for Garch Models by the Least Absolute Deviation Estimation," Journal of Time Series Analysis, Wiley Blackwell, vol. 41(1), pages 21-40, January.
    27. Hong, Yongmiao & Lee, Tae-Hwy, 2003. "Diagnostic Checking For The Adequacy Of Nonlinear Time Series Models," Econometric Theory, Cambridge University Press, vol. 19(6), pages 1065-1121, December.
    28. 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.
    29. Peter Hall & Qiwei Yao, 2003. "Inference in Arch and Garch Models with Heavy--Tailed Errors," Econometrica, Econometric Society, vol. 71(1), pages 285-317, January.
    30. Roger Koenker, 2017. "Quantile regression 40 years on," CeMMAP working papers 36/17, Institute for Fiscal Studies.
    31. Ke Zhu & Wai Keung Li, 2015. "A New Pearson-Type QMLE for Conditionally Heteroscedastic Models," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 33(4), pages 552-565, October.
    32. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
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