IDEAS home Printed from
   My bibliography  Save this article

Asymptotics Of Spectral Density Estimates


  • Liu, Weidong
  • Wu, Wei Biao


We consider nonparametric estimation of spectral densities of stationary processes, a fundamental problem in spectral analysis of time series. Under natural and easily verifiable conditions, we obtain consistency and asymptotic normality of spectral density estimates. Asymptotic distribution of maximum deviations of the spectral density estimates is also derived. The latter result sheds new light on the classical problem of tests of white noises.

Suggested Citation

  • Liu, Weidong & Wu, Wei Biao, 2010. "Asymptotics Of Spectral Density Estimates," Econometric Theory, Cambridge University Press, vol. 26(04), pages 1218-1245, August.
  • Handle: RePEc:cup:etheor:v:26:y:2010:i:04:p:1218-1245_99

    Download full text from publisher

    File URL:
    File Function: link to article abstract page
    Download Restriction: no


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

    Cited by:

    1. Politis, Dimitris, 2012. "On The Behavior Of Nonparametric Density And Spectral Density Estimators At Zero Points Of Their Support," University of California at San Diego, Economics Working Paper Series qt40g0z0tz, Department of Economics, UC San Diego.
    2. 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.
    3. Forni, Mario & Hallin, Marc & Lippi, Marco & Zaffaroni, Paolo, 2017. "Dynamic factor models with infinite-dimensional factor space: Asymptotic analysis," Journal of Econometrics, Elsevier, vol. 199(1), pages 74-92.
    4. Horváth, Lajos & Rice, Gregory & Whipple, Stephen, 2016. "Adaptive bandwidth selection in the long run covariance estimator of functional time series," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 676-693.
    5. Seok Young Hong & Oliver Linton & Hui Jun Zhang, 2014. "Multivariate Variance Ratio Statistics," Cambridge Working Papers in Economics 1459, Faculty of Economics, University of Cambridge.
    6. Berkes, István & Horváth, Lajos & Rice, Gregory, 2016. "On the asymptotic normality of kernel estimators of the long run covariance of functional time series," Journal of Multivariate Analysis, Elsevier, vol. 144(C), pages 150-175.
    7. Seok Young Hong & Oliver Linton & Hui Jun Zhang, 2015. "An investigation into Multivariate Variance Ratio Statistics and their application to Stock Market Predictability," Cambridge Working Papers in Economics 1552, Faculty of Economics, University of Cambridge.
    8. Horváth, Lajos & Reeder, Ron, 2012. "Detecting changes in functional linear models," Journal of Multivariate Analysis, Elsevier, vol. 111(C), pages 310-334.
    9. repec:bla:scjsta:v:44:y:2017:i:4:p:866-898 is not listed on IDEAS
    10. Efstathios Paparoditis & Dimitris N. Politis, 2016. "A Note on the Behaviour of Nonparametric Density and Spectral Density Estimators at Zero Points of their Support," Journal of Time Series Analysis, Wiley Blackwell, vol. 37(2), pages 182-194, 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:cup:etheor:v:26:y:2010:i:04:p:1218-1245_99. 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: (Keith Waters). 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.