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Quantile‐frequency analysis and spectral measures for diagnostic checks of time series with nonlinear dynamics

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  • Ta‐Hsin Li

Abstract

Nonlinear dynamic volatility has been observed in many financial time series. The recently proposed quantile periodogram offers an alternative way to examine this phenomena in the frequency domain. The quantile periodogram is constructed from trigonometric quantile regression of time series data at different frequencies and quantile levels, enabling the quantile‐frequency analysis (QFA) of nonlinear serial dependence. This paper introduces some spectral measures based on the quantile periodogram for diagnostic checks of financial time series models and for model‐based discriminant analysis. A simulation‐based parametric bootstrapping technique is employed to compute the p‐values of the spectral measures. The usefulness of the proposed method is demonstrated by a simulation study and a motivating application using the daily log returns of the S&P 500 index together with GARCH‐type models. The results show that the QFA method is able to provide additional insights into the goodness of fit of these financial time series models that may have been missed by conventional tests. The results also show that the QFA method offers a more informative way of discriminant analysis for detecting regime changes in financial time series.

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  • Ta‐Hsin Li, 2021. "Quantile‐frequency analysis and spectral measures for diagnostic checks of time series with nonlinear dynamics," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 70(2), pages 270-290, March.
  • Handle: RePEc:bla:jorssc:v:70:y:2021:i:2:p:270-290
    DOI: 10.1111/rssc.12458
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    1. Schwert, G William, 1990. "Stock Volatility and the Crash of '87," The Review of Financial Studies, Society for Financial Studies, vol. 3(1), pages 77-102.
    2. Higgins, Matthew L & Bera, Anil K, 1992. "A Class of Nonlinear ARCH Models," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 33(1), pages 137-158, February.
    3. Asger Lunde & Peter R. Hansen, 2005. "A forecast comparison of volatility models: does anything beat a GARCH(1,1)?," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 20(7), pages 873-889.
    4. Andrew Ang & Allan Timmermann, 2012. "Regime Changes and Financial Markets," Annual Review of Financial Economics, Annual Reviews, vol. 4(1), pages 313-337, October.
    5. Ding, Zhuanxin & Granger, Clive W. J. & Engle, Robert F., 1993. "A long memory property of stock market returns and a new model," Journal of Empirical Finance, Elsevier, vol. 1(1), pages 83-106, June.
    6. Efstathios Paparoditis & Dimitris N. Politis, 1999. "The Local Bootstrap for Periodogram Statistics," Journal of Time Series Analysis, Wiley Blackwell, vol. 20(2), pages 193-222, March.
    7. Ta‐Hsin Li, 2012. "On robust spectral analysis by least absolute deviations," Journal of Time Series Analysis, Wiley Blackwell, vol. 33(2), pages 298-303, March.
    8. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    9. Howard D. Bondell & Brian J. Reich & Huixia Wang, 2010. "Noncrossing quantile regression curve estimation," Biometrika, Biometrika Trust, vol. 97(4), pages 825-838.
    10. Glosten, Lawrence R & Jagannathan, Ravi & Runkle, David E, 1993. "On the Relation between the Expected Value and the Volatility of the Nominal Excess Return on Stocks," Journal of Finance, American Finance Association, vol. 48(5), pages 1779-1801, December.
    11. Lian, Heng & Meng, Jie & Fan, Zengyan, 2015. "Simultaneous estimation of linear conditional quantiles with penalized splines," Journal of Multivariate Analysis, Elsevier, vol. 141(C), pages 1-21.
    12. Yongmiao Hong, 2000. "Generalized spectral tests for serial dependence," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(3), pages 557-574.
    13. Li, Ta-Hsin, 2008. "Laplace Periodogram for Time Series Analysis," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 757-768, June.
    14. Hsiao-Yun Huang & Hernando Ombao & David S. Stoffer, 2004. "Discrimination and Classification of Nonstationary Time Series Using the SLEX Model," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 763-774, January.
    15. Zakoian, Jean-Michel, 1994. "Threshold heteroskedastic models," Journal of Economic Dynamics and Control, Elsevier, vol. 18(5), pages 931-955, September.
    16. Ria Van Hecke & Stanislav Volgushev & Holger Dette, 2018. "Fourier Analysis of Serial Dependence Measures," Journal of Time Series Analysis, Wiley Blackwell, vol. 39(1), pages 75-89, January.
    17. 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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    2. Lars Arne Jordanger & Dag Tjøstheim, 2023. "Local Gaussian Cross-Spectrum Analysis," Econometrics, MDPI, vol. 11(2), pages 1-27, April.

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