IDEAS home Printed from https://ideas.repec.org/a/bla/jorssb/v68y2006i4p611-634.html
   My bibliography  Save this article

Haar-Fisz estimation of evolutionary wavelet spectra

Author

Listed:
  • Piotr Fryzlewicz
  • Guy P. Nason

Abstract

We propose a new 'Haar-Fisz' technique for estimating the time-varying, piecewise constant local variance of a locally stationary Gaussian time series. We apply our technique to the estimation of the spectral structure in the locally stationary wavelet model. Our method combines Haar wavelets and the variance stabilizing Fisz transform. The resulting estimator is mean square consistent, rapidly computable and easy to implement, and performs well in practice. We also introduce the 'Haar-Fisz transform', a device for stabilizing the variance of scaled "χ"-super-2-data and bringing their distribution close to Gaussianity. Copyright 2006 Royal Statistical Society.

Suggested Citation

  • Piotr Fryzlewicz & Guy P. Nason, 2006. "Haar-Fisz estimation of evolutionary wavelet spectra," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(4), pages 611-634.
  • Handle: RePEc:bla:jorssb:v:68:y:2006:i:4:p:611-634
    as

    Download full text from publisher

    File URL: http://www.blackwell-synergy.com/doi/abs/10.1111/j.1467-9868.2006.00558.x
    File Function: link to full text
    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.

    Citations

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


    Cited by:

    1. Lars Winkelmann, 2013. "Quantitative forward guidance and the predictability of monetary policy - A wavelet based jump detection approach -," SFB 649 Discussion Papers SFB649DP2013-016, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    2. Sanderson, Jean & Fryzlewicz, Piotr & Jones, M. W., 2010. "Estimating linear dependence between nonstationary time series using the locally stationary wavelet model," LSE Research Online Documents on Economics 29141, London School of Economics and Political Science, LSE Library.
    3. Zhou Zhou, 2013. "Inference for non-stationary time-series autoregression," Journal of Time Series Analysis, Wiley Blackwell, vol. 34(4), pages 508-516, July.
    4. Fryzlewicz, Piotr & Cho, Haeran, 2014. "Multiple change-point detection for high-dimensional time series via sparsified binary segmentation," LSE Research Online Documents on Economics 57147, London School of Economics and Political Science, LSE Library.
    5. Piotr Fryzlewicz & Guy P. Nason & Rainer von Sachs, 2008. "A wavelet-Fisz approach to spectrum estimation," Journal of Time Series Analysis, Wiley Blackwell, vol. 29(5), pages 868-880, September.
    6. Guy Nason, 2013. "A test for second-order stationarity and approximate confidence intervals for localized autocovariances for locally stationary time series," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 75(5), pages 879-904, November.
    7. Fryzlewicz, Piotr & Delouille, V´eronique & Nason, Guy P., 2007. "GOES-8 X-ray sensor variance stabilization using the multiscale data-driven Haar-Fisz transform," LSE Research Online Documents on Economics 25221, London School of Economics and Political Science, LSE Library.
    8. Triantafyllopoulos, K. & Nason, G.P., 2009. "A note on state space representations of locally stationary wavelet time series," Statistics & Probability Letters, Elsevier, vol. 79(1), pages 50-54, January.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    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:bla:jorssb:v:68:y:2006:i:4:p:611-634. 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: (Wiley-Blackwell Digital Licensing) or (Christopher F. Baum). General contact details of provider: http://edirc.repec.org/data/rssssea.html .

    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.