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Haar-Fisz estimation of evolutionary wavelet spectra

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  • Fryzlewicz, Piotr
  • Nason, Guy P.

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 χ2-data and bringing their distribution close to Gaussianity.

Suggested Citation

  • 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.
    • Handle: RePEc:ehl:lserod:25227
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    References listed on IDEAS

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    7. Piotr Fryzlewicz & Theofanis Sapatinas & Suhasini Subba Rao, 2006. "A Haar--Fisz technique for locally stationary volatility estimation," Biometrika, Biometrika Trust, vol. 93(3), pages 687-704, September.
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    11. 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.
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    Citations

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    Cited by:

    1. Embleton, Jonathan & Knight, Marina I. & Ombao, Hernando, 2022. "Wavelet testing for a replicate-effect within an ordered multiple-trial experiment," Computational Statistics & Data Analysis, Elsevier, vol. 174(C).
    2. I A Eckley & G P Nason, 2018. "A test for the absence of aliasing or local white noise in locally stationary wavelet time series," Biometrika, Biometrika Trust, vol. 105(4), pages 833-848.
    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. 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.
    5. Winkelmann, Lars, 2010. "The Norges Bank's key rate projections and the news element of monetary policy: A wavelet based jump detection approach," SFB 649 Discussion Papers 2010-062, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    6. Zhelin Huang & Ngai Hang Chan, 2020. "Walsh Fourier Transform of Locally Stationary Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 41(2), pages 312-340, March.
    7. Winkelmann, Lars, 2013. "Quantitative forward guidance and the predictability of monetary policy: A wavelet based jump detection approach," SFB 649 Discussion Papers 2013-016, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    8. Barigozzi, Matteo & Cho, Haeran & Fryzlewicz, Piotr, 2018. "Simultaneous multiple change-point and factor analysis for high-dimensional time series," Journal of Econometrics, Elsevier, vol. 206(1), pages 187-225.
    9. Antonis A. Michis & Guy P. Nason, 2017. "Case study: shipping trend estimation and prediction via multiscale variance stabilisation," Journal of Applied Statistics, Taylor & Francis Journals, vol. 44(15), pages 2672-2684, November.
    10. repec:hum:wpaper:sfb649dp2013-016 is not listed on IDEAS
    11. 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.
    12. Zhou Zhou, 2013. "Inference for non-stationary time-series autoregression," Journal of Time Series Analysis, Wiley Blackwell, vol. 34(4), pages 508-516, July.
    13. Cho, Haeran & Fryzlewicz, Piotr, 2015. "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.
    14. Cardinali Alessandro & Nason Guy P, 2011. "Costationarity of Locally Stationary Time Series," Journal of Time Series Econometrics, De Gruyter, vol. 2(2), pages 1-35, January.
    15. 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.

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    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General

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