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Choice of thresholds for wavelet shrinkage estimate of the spectrum

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  • 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
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    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. 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).
    3. 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.
    4. 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.
    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. 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.
    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. 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.

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