Haar-Fisz estimation of evolutionary wavelet spectra. 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 $chi^2$-data and bringing their distribution close to Gaussianity.

References in zbMATH (referenced in 17 articles , 1 standard article )

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  1. Hargreaves, Jessica K.; Knight, Marina I.; Pitchford, Jon W.; Oakenfull, Rachael J.; Chawla, Sangeeta; Munns, Jack; Davis, Seth J.: Wavelet spectral testing: application to nonstationary circadian rhythms (2019)
  2. Barigozzi, Matteo; Cho, Haeran; Fryzlewicz, Piotr: Simultaneous multiple change-point and factor analysis for high-dimensional time series (2018)
  3. Cardinali, Alessandro; Nason, Guy P.: Practical powerful wavelet packet tests for second-order stationarity (2018)
  4. Nelson, J. D. B.; Gibberd, A. J.; Nafornita, C.; Kingsbury, N.: The locally stationary dual-tree complex wavelet model (2018)
  5. Norwood, Ben; Killick, Rebecca: Long memory and changepoint models: a spectral classification procedure (2018)
  6. Michis, Antonis A.; Nason, Guy P.: Case study: shipping trend estimation and prediction via multiscale variance stabilisation (2017)
  7. Eckley, Idris A.; Nason, Guy P.: Spectral correction for locally stationary Shannon wavelet processes (2014)
  8. Fryzlewicz, P.: High-dimensional volatility matrix estimation via wavelets and thresholding (2013)
  9. Killick, R.; Eckley, I. A.; Jonathan, P.: A wavelet-based approach for detecting changes in second order structure within nonstationary time series (2013)
  10. Zhou, Zhou: Inference for non-stationary time-series autoregression (2013)
  11. Knight, Marina I.; Nunes, Matthew A.; Nason, Guy P.: Spectral estimation for locally stationary time series with missing observations (2012)
  12. Cardinali, Alessandro; Nason, Guy P.: Costationarity of locally stationary time series (2010)
  13. Sanderson, J.; Fryzlewicz, P.; Jones, M. W.: Estimating linear dependence between nonstationary time series using the locally stationary wavelet model (2010)
  14. Fryzlewicz, Piotr; Nason, Guy P.; Von Sachs, Rainer: A wavelet-Fisz approach to spectrum estimation (2008)
  15. Schmidt, Thorsten; Xu, Ling: Some limit results on the Haar-Fisz transform for inhomogeneous Poisson signals (2008)
  16. van Bellegem, Sébastien; von Sachs, Rainer: Locally adaptive estimation of evolutionary wavelet spectra (2008)
  17. Fryzlewicz, Piotr; Nason, Guy P.: Haar-Fisz estimation of evolutionary wavelet spectra (2006)