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Haar-Fisz estimation of evolutionary wavelet spectra


  • Piotr Fryzlewicz
  • Guy P. Nason


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

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    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.

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