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Smoothing the wavelet periodogram using the Haar-Fisz transform

By Piotr Fryzlewicz and Guy P. Nason

Abstract

The wavelet periodogram is hard to smooth because of the low signal-to-noise ratio and non-stationary covariance structure. This article introduces a method for smoothing a local wavelet periodogram by applying a Haar-Fisz transform which approximately Gaussianizes and approximately stabilizes the variance of the periodogram. Consequently, smoothing the transformed periodogram can take advantage of the wide variety of existing techniques suitable for homogeneous Gaussian data. This article demonstrates the superiority of the new method over existing methods and supplies theory that proves the Gaussianizing, variance stabilizing and decorrelation properties of the Haar-Fisz transform

Topics: HA Statistics
Publisher: Department of Mathematics, University of Bristol
Year: 2004
OAI identifier: oai:eprints.lse.ac.uk:25231
Provided by: LSE Research Online
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    Citations

    1. (1989). A theory for multiresolution signal decomposition: the wavelet representation. doi
    2. (1995). Adapting to unknown smoothness via wavelet shrinkage. doi
    3. (1998). Adaptive covariance estimation of locally stationary processes. doi
    4. (1999). Awavelet analysis fortime series.
    5. (1989). Contributions to evolutionary spectral theory. doi
    6. (1998). Econometric analysis of locally stationary time series models.
    7. (1965). Evolutionary spectra and non-stationary processes.
    8. (2001). Forecasting multifractal volatility. doi
    9. (2003). Forecasting non-stationary time series by wavelet process modelling. doi
    10. (2002). Modelling and forecasting ļ¬nancial log-returns as locally stationary wavelet processes.
    11. (2000). Non-parametric curve estimation by wavelet thresholding with locally stationary errors. doi
    12. (2001). Nonparametric regression with correlated errors. doi
    13. (1996). On the Kullback-Leibler information divergence of locally stationary processes. doi
    14. (2004). Real nonparametric regression using complex wavelets. doi
    15. (1979). Some extensions in the evolutionary spectral analysis of a stochastic process.
    16. (2002). Some statistical applications for locally stationary processes.
    17. (1981). Spectral Analysis and Time Series. doi
    18. (1998). Spectrum estimation by wavelet thresholding of multitaper estimators. doi
    19. (1999). Statistical Modeling by Wavelets. doi
    20. (1994). Stochastic Limit Theory. doi
    21. (1992). Ten Lectures on Wavelets. doi
    22. (2000). The evolutionary spectra of a harmonizable process. doi
    23. (1955). The limiting distribution of a function of two independent random variables and its statistical application.
    24. (2002). The SLEX model of a non-stationary random process.
    25. (1995). The stationary wavelet transform and some statistical applications. doi
    26. (1995). Translation-invariant de-noising. doi
    27. (2000). Wavelet processes and adaptive estimation of the evolutionary wavelet spectrum. doi
    28. (1997). Wavelet threshold estimators for data with correlated noise. doi
    29. (1995). Wavelet thresholding: beyond the Gaussian iid situation. doi

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