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Adaptive inference for a semiparametric generalized autoregressive conditional heteroskedasticity model

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  • Feiyu Jiang
  • Dong Li
  • Ke Zhu

Abstract

This paper considers a semiparametric generalized autoregressive conditional heteroskedasticity (S-GARCH) model. For this model, we first estimate the time-varying long run component for unconditional variance by the kernel estimator, and then estimate the non-time-varying parameters in GARCH-type short run component by the quasi maximum likelihood estimator (QMLE). We show that the QMLE is asymptotically normal with the parametric convergence rate. Next, we construct a Lagrange multiplier test for linear parameter constraint and a portmanteau test for model checking, and obtain their asymptotic null distributions. Our entire statistical inference procedure works for the non-stationary data with two important features: first, our QMLE and two tests are adaptive to the unknown form of the long run component; second, our QMLE and two tests share the same efficiency and testing power as those in variance targeting method when the S-GARCH model is stationary.

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  • Feiyu Jiang & Dong Li & Ke Zhu, 2019. "Adaptive inference for a semiparametric generalized autoregressive conditional heteroskedasticity model," Papers 1907.04147, arXiv.org, revised Oct 2020.
    • Handle: RePEc:arx:papers:1907.04147
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    1. Francq, Christian & Zakoïan, Jean-Michel, 2009. "Testing the Nullity of GARCH Coefficients: Correction of the Standard Tests and Relative Efficiency Comparisons," Journal of the American Statistical Association, American Statistical Association, vol. 104(485), pages 313-324.
    2. Robert F. Engle & Jose Gonzalo Rangel, 2008. "The Spline-GARCH Model for Low-Frequency Volatility and Its Global Macroeconomic Causes," The Review of Financial Studies, Society for Financial Studies, vol. 21(3), pages 1187-1222, May.
    3. 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.
    4. Hafner, Christian M. & Linton, Oliver, 2010. "Efficient estimation of a multivariate multiplicative volatility model," Journal of Econometrics, Elsevier, vol. 159(1), pages 55-73, November.
    5. Christian Francq & Lajos Horváth, 2011. "Merits and Drawbacks of Variance Targeting in GARCH Models," Journal of Financial Econometrics, Oxford University Press, vol. 9(4), pages 619-656.
    6. Bruce E. Hansen, 2001. "The New Econometrics of Structural Change: Dating Breaks in U.S. Labour Productivity," Journal of Economic Perspectives, American Economic Association, vol. 15(4), pages 117-128, Fall.
    7. Cavaliere, Giuseppe & Taylor, A.M. Robert, 2007. "Testing for unit roots in time series models with non-stationary volatility," Journal of Econometrics, Elsevier, vol. 140(2), pages 919-947, October.
    8. Xu, Ke-Li & Phillips, Peter C.B., 2008. "Adaptive estimation of autoregressive models with time-varying variances," Journal of Econometrics, Elsevier, vol. 142(1), pages 265-280, January.
    9. 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.
    10. Robinson, P M, 1987. "Asymptotically Efficient Estimation in the Presence of Heteroskedasticity of Unknown Form," Econometrica, Econometric Society, vol. 55(4), pages 875-891, July.
    11. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    12. Escanciano, J. Carlos & Lobato, Ignacio N., 2009. "An automatic Portmanteau test for serial correlation," Journal of Econometrics, Elsevier, vol. 151(2), pages 140-149, August.
    13. Fryzlewicz, Piotr & Sapatinas, Theofanis & Subba Rao, Suhasini, 2008. "Normalized least-squares estimation in time-varying ARCH models," LSE Research Online Documents on Economics 25187, London School of Economics and Political Science, LSE Library.
    14. W. K. Li & T. K. Mak, 1994. "On The Squared Residual Autocorrelations In Non‐Linear Time Series With Conditional Heteroskedasticity," Journal of Time Series Analysis, Wiley Blackwell, vol. 15(6), pages 627-636, November.
    15. Valentin Patilea & Hamdi Raïssi, 2014. "Testing Second-Order Dynamics for Autoregressive Processes in Presence of Time-Varying Variance," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(507), pages 1099-1111, September.
    16. Feng, Yuanhua, 2004. "Simultaneously Modeling Conditional Heteroskedasticity And Scale Change," Econometric Theory, Cambridge University Press, vol. 20(3), pages 563-596, June.
    17. Amado, Cristina & Teräsvirta, Timo, 2013. "Modelling volatility by variance decomposition," Journal of Econometrics, Elsevier, vol. 175(2), pages 142-153.
    18. Lionel Truquet, 2017. "Parameter stability and semiparametric inference in time varying auto-regressive conditional heteroscedasticity models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 79(5), pages 1391-1414, November.
    19. Cai, Zongwu, 2007. "Trending time-varying coefficient time series models with serially correlated errors," Journal of Econometrics, Elsevier, vol. 136(1), pages 163-188, January.
    20. repec:hal:journl:peer-00732539 is not listed on IDEAS
    21. Cătălin Stărică & Clive Granger, 2005. "Nonstationarities in Stock Returns," The Review of Economics and Statistics, MIT Press, vol. 87(3), pages 503-522, August.
    22. Chen, Bin & Hong, Yongmiao, 2016. "Detecting For Smooth Structural Changes In Garch Models," Econometric Theory, Cambridge University Press, vol. 32(3), pages 740-791, June.
    23. Zhou Zhou & Xiaofeng Shao, 2013. "Inference for linear models with dependent errors," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 75(2), pages 323-343, March.
    24. Thomas Mikosch & Cătălin Stărică, 2004. "Nonstationarities in Financial Time Series, the Long-Range Dependence, and the IGARCH Effects," The Review of Economics and Statistics, MIT Press, vol. 86(1), pages 378-390, February.
    25. 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.
    26. Halbert White, 2000. "A Reality Check for Data Snooping," Econometrica, Econometric Society, vol. 68(5), pages 1097-1126, September.
    27. Carrasco, Marine & Chen, Xiaohong, 2002. "Mixing And Moment Properties Of Various Garch And Stochastic Volatility Models," Econometric Theory, Cambridge University Press, vol. 18(1), pages 17-39, February.
    28. Vogt, Michael, 2015. "Testing For Structural Change In Time-Varying Nonparametric Regression Models," Econometric Theory, Cambridge University Press, vol. 31(4), pages 811-859, August.
    29. 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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    Cited by:

    1. Jiang, Feiyu & Li, Dong & Zhu, Ke, 2021. "Adaptive inference for a semiparametric generalized autoregressive conditional heteroskedasticity model," Journal of Econometrics, Elsevier, vol. 224(2), pages 306-329.

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