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Quantile Periodograms

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  • Ta-Hsin Li

Abstract

Two periodogram-like functions, called quantile periodograms, are introduced for spectral analysis of time series. The quantile periodograms are constructed from trigonometric quantile regression and motivated by different interpretations of the ordinary periodogram. Analytical and numerical results demonstrate the capability of the quantile periodograms for detecting hidden periodicity in the quantiles and for providing an additional view of time-series data. A connection between the quantile periodograms and the so-called level-crossing spectrum is established through an asymptotic analysis.

Suggested Citation

  • Ta-Hsin Li, 2012. "Quantile Periodograms," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(498), pages 765-776, June.
    • Handle: RePEc:taf:jnlasa:v:107:y:2012:i:498:p:765-776
    DOI: 10.1080/01621459.2012.682815
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    Citations

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    Cited by:

    1. Stefan Birr & Holger Dette & Marc Hallin & Tobias Kley & Stanislav Volgushev, 2016. "On Wigner-Ville Spectra and the Unicity of Time-Varying Quantile-Based Spectral Densities," Working Papers ECARES ECARES 2016-38, ULB -- Universite Libre de Bruxelles.
    2. Lee, Ji Hyung & Linton, Oliver & Whang, Yoon-Jae, 2020. "Quantilograms Under Strong Dependence," Econometric Theory, Cambridge University Press, vol. 36(3), pages 457-487, June.
    3. Jin, Lei, 2021. "Robust tests for time series comparison based on Laplace periodograms," Computational Statistics & Data Analysis, Elsevier, vol. 160(C).
    4. Stefan Birr & Stanislav Volgushev & Tobias Kley & Holger Dette & Marc Hallin, 2017. "Quantile spectral analysis for locally stationary time series," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 79(5), pages 1619-1643, November.
    5. Aviral Kumar Tiwari & Muhammad Shahbaz & Rabeh Khalfaoui & Rizwan Ahmed & Shawkat Hammoudeh, 2024. "Directional predictability from energy markets to exchange rates and stock markets in the emerging market countries (E7 + 1): New evidence from cross‐quantilogram approach," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 29(1), pages 719-789, January.
    6. Ta-Hsin Li, 2014. "Quantile Periodogram And Time-Dependent Variance," Journal of Time Series Analysis, Wiley Blackwell, vol. 35(4), pages 322-340, July.
    7. Thilo A. Schmitt & Rudi Schafer & Holger Dette & Thomas Guhr, 2015. "Quantile Correlations: Uncovering temporal dependencies in financial time series," Papers 1507.04990, arXiv.org.
    8. Yuichi Goto & Tobias Kley & Ria Van Hecke & Stanislav Volgushev & Holger Dette & Marc Hallin, 2021. "The Integrated Copula Spectrum," Working Papers ECARES 2021-29, ULB -- Universite Libre de Bruxelles.
    9. Jozef Baruník & Tobias Kley, 2019. "Quantile coherency: A general measure for dependence between cyclical economic variables," The Econometrics Journal, Royal Economic Society, vol. 22(2), pages 131-152.
    10. Han, Heejoon & Linton, Oliver & Oka, Tatsushi & Whang, Yoon-Jae, 2016. "The cross-quantilogram: Measuring quantile dependence and testing directional predictability between time series," Journal of Econometrics, Elsevier, vol. 193(1), pages 251-270.
    11. Zhang, Shibin, 2019. "Bayesian copula spectral analysis for stationary time series," Computational Statistics & Data Analysis, Elsevier, vol. 133(C), pages 166-179.
    12. Ta-Hsin Li, 2019. "Quantile-Frequency Analysis and Spectral Divergence Metrics for Diagnostic Checks of Time Series With Nonlinear Dynamics," Papers 1908.02545, arXiv.org.
    13. Yaeji Lim & Hee-Seok Oh, 2022. "Quantile spectral analysis of long-memory processes," Empirical Economics, Springer, vol. 62(3), pages 1245-1266, March.
    14. Thilo A. Schmitt & Rudi Schäfer & Holger Dette & Thomas Guhr, 2015. "Quantile Correlations: Uncovering Temporal Dependencies In Financial Time Series," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 18(07), pages 1-16, November.
    15. Chen, Tianbo & Sun, Ying & Li, Ta-Hsin, 2021. "A semi-parametric estimation method for the quantile spectrum with an application to earthquake classification using convolutional neural network," Computational Statistics & Data Analysis, Elsevier, vol. 154(C).
    16. Yan Liu, 2017. "Statistical inference for quantiles in the frequency domain," Statistical Inference for Stochastic Processes, Springer, vol. 20(3), pages 369-386, October.
    17. Yaeji Lim & Hee-Seok Oh, 2016. "Composite Quantile Periodogram for Spectral Analysis," Journal of Time Series Analysis, Wiley Blackwell, vol. 37(2), pages 195-221, March.

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