IDEAS home Printed from
   My bibliography  Save this article

Quantile Periodograms


  • Ta-Hsin Li


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

    Download full text from publisher

    File URL:
    Download Restriction: Access to full text is restricted to subscribers.

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    1. 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.
    2. James H. Stock & Mark W. Watson, 2003. "Has the Business Cycle Changed and Why?," NBER Chapters,in: NBER Macroeconomics Annual 2002, Volume 17, pages 159-230 National Bureau of Economic Research, Inc.
    3. Francis X. Diebold & Lutz Kilian, 2001. "Measuring predictability: theory and macroeconomic applications," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 16(6), pages 657-669.
    4. Alessandra Luati & Tommaso Proietti, 2010. "Hyper-spherical and elliptical stochastic cycles," Journal of Time Series Analysis, Wiley Blackwell, vol. 31(3), pages 169-181, May.
    5. Kasahara, Yukio & Pourahmadi, Mohsen & Inoue, Akihiko, 2009. "Duals of random vectors and processes with applications to prediction problems with missing values," Statistics & Probability Letters, Elsevier, vol. 79(14), pages 1637-1646, July.
    6. Baillie, Richard T., 1996. "Long memory processes and fractional integration in econometrics," Journal of Econometrics, Elsevier, vol. 73(1), pages 5-59, July.
    7. Nidhan Choudhuri & Subhashis Ghosal & Anindya Roy, 2004. "Bayesian Estimation of the Spectral Density of a Time Series," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 1050-1059, December.
    8. Hannan, E J & Terrell, R D & Tuckwell, N E, 1970. "The Seasonal Adjustment of Economic Time Series," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 11(1), pages 24-52, February.
    Full references (including those not matched with items on IDEAS)


    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.

    Cited by:

    1. 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.
    2. Ta-Hsin Li, 2014. "Quantile Periodogram And Time-Dependent Variance," Journal of Time Series Analysis, Wiley Blackwell, vol. 35(4), pages 322-340, July.
    3. Thilo A. Schmitt & Rudi Schafer & Holger Dette & Thomas Guhr, 2015. "Quantile Correlations: Uncovering temporal dependencies in financial time series," Papers 1507.04990,
    4. Jozef Barun'ik & Tobias Kley, 2015. "Quantile Cross-Spectral Measures of Dependence between Economic Variables," Papers 1510.06946,
    5. 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.
    6. 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.
    7. 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.
    8. repec:spr:sistpr:v:20:y:2017:i:3:d:10.1007_s11203-017-9166-4 is not listed on IDEAS
    9. 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.

    More about this item


    Access and download statistics


    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:taf:jnlasa:v:107:y:2012:i:498:p:765-776. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Chris Longhurst). General contact details of provider: .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.