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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.

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  • 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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    1. Hernando Ombao & Jonathan Raz & Rainer von Sachs & Wensheng Guo, 2002. "The SLEX Model of a Non-Stationary Random Process," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 54(1), pages 171-200, March.
    2. G. P. Nason & R. Von Sachs & G. Kroisandt, 2000. "Wavelet processes and adaptive estimation of the evolutionary wavelet spectrum," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(2), pages 271-292.
    3. Davis, Richard A. & Lee, Thomas C.M. & Rodriguez-Yam, Gabriel A., 2006. "Structural Break Estimation for Nonstationary Time Series Models," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 223-239, March.
    4. Guy Melard & Annie Herteleer, 1989. "Contributions to the evolutionary spectral theory," ULB Institutional Repository 2013/13708, ULB -- Universite Libre de Bruxelles.
    5. Jones, M. C., 1987. "On moments of ratios of quadratic forms in normal variables," Statistics & Probability Letters, Elsevier, vol. 6(2), pages 129-136, November.
    6. Rainer Von Sachs & Brenda Macgibbon, 2000. "Non‐parametric Curve Estimation by Wavelet Thresholding with Locally Stationary Errors," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 27(3), pages 475-499, September.
    7. Calvet, Laurent & Fisher, Adlai, 2001. "Forecasting multifractal volatility," Journal of Econometrics, Elsevier, vol. 105(1), pages 27-58, November.
    8. Ghazal, G. A., 1994. "Moments of the ratio of two dependent quadratic forms," Statistics & Probability Letters, Elsevier, vol. 20(4), pages 313-319, July.
    9. 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.
    10. Guy Mélard & Annie Herteleer‐de Schutter, 1989. "Contributions To Evolutionary Spectral Theory," Journal of Time Series Analysis, Wiley Blackwell, vol. 10(1), pages 41-63, January.
    11. 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.
    12. Dahlhaus, R., 1996. "On the Kullback-Leibler information divergence of locally stationary processes," Stochastic Processes and their Applications, Elsevier, vol. 62(1), pages 139-168, March.
    13. 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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    Cited by:

    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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).
    7. 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.
    8. 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.
    9. 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.
    10. 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.
    11. Zhou Zhou, 2013. "Inference for non-stationary time-series autoregression," Journal of Time Series Analysis, Wiley Blackwell, vol. 34(4), pages 508-516, July.
    12. 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.
    13. 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.

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

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