IDEAS home Printed from https://ideas.repec.org/a/bla/jtsera/v18y1997i3p231-251.html
   My bibliography  Save this article

Choice of thresholds for wavelet shrinkage estimate of the spectrum

Author

Listed:
  • Hong‐Ye Gao

Abstract

We study the problem of estimating the log‐spectrum of a stationary Gaussian time series by thresholding the empirical wavelet coefficients. We propose the use of thresholds tj,n depending on sample size n, wavelet basis ψ and resolution level j. At fine resolution levels (j = 1, 2, ...) we propose t j,n = αj log n where {αj} are level‐dependent constants and at coarse levels (j≫ 1) t j,n = (π/√3)(log n)1/2. The purpose of this thresholding level is to make the reconstructed log‐spectrum as nearly noise‐free as possible. In addition to being pleasant from a visual point of view, the noise‐free character leads to attractive theoretical properties over a wide range of smoothness assumptions. Previous proposals set much smaller thresholds and did not enjoy these properties.

Suggested Citation

  • Hong‐Ye Gao, 1997. "Choice of thresholds for wavelet shrinkage estimate of the spectrum," Journal of Time Series Analysis, Wiley Blackwell, vol. 18(3), pages 231-251, May.
    • Handle: RePEc:bla:jtsera:v:18:y:1997:i:3:p:231-251
    DOI: 10.1111/1467-9892.00048
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/1467-9892.00048
    Download Restriction: no
    File URL: https://libkey.io/10.1111/1467-9892.00048?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    Citations

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


    Cited by:

    1. Lada, Emily K. & Wilson, James R., 2006. "A wavelet-based spectral procedure for steady-state simulation analysis," European Journal of Operational Research, Elsevier, vol. 174(3), pages 1769-1801, November.
    2. Yang, Lu, 2019. "Connectedness of economic policy uncertainty and oil price shocks in a time domain perspective," Energy Economics, Elsevier, vol. 80(C), pages 219-233.
    3. 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.
    4. Fryzlewicz, Piotr & Nason, Guy P., 2006. "Haar-Fisz estimation of evolutionary wavelet spectra," LSE Research Online Documents on Economics 25227, London School of Economics and Political Science, LSE Library.
    5. Chau, Van Vinh & von Sachs, Rainer, 2016. "Functional mixed effects wavelet estimation for spectra of replicated time series," LIDAM Discussion Papers ISBA 2016013, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    6. Fryzlewicz, Piotr & Nason, Guy P. & von Sachs, Rainer, 2008. "A wavelet-Fisz approach to spectrum estimation," LSE Research Online Documents on Economics 25186, London School of Economics and Political Science, LSE Library.
    7. Fryzlewicz, Piotr & Sapatinas, Theofanis & Subba Rao, Suhasini, 2006. "A Haar-Fisz technique for locally stationary volatility estimation," LSE Research Online Documents on Economics 25225, London School of Economics and Political Science, LSE Library.
    8. von Sachs, Rainer, 2019. "Spectral Analysis of Multivariate Time Series," LIDAM Discussion Papers ISBA 2019008, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    9. Debashis Mondal & Donald Percival, 2012. "M-estimation of wavelet variance," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 64(1), pages 27-53, February.

    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:jtsera:v:18:y:1997:i:3:p:231-251. See general information about how to correct material in RePEc.

    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 bibliographic 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.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Wiley Content Delivery (email available below). General contact details of provider: http://www.blackwellpublishing.com/journal.asp?ref=0143-9782 .

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

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.