The paper by G.P. Nason and B.W. Silverman explores the statistical applications of wavelets, focusing on the stationary wavelet transform (SWT). The authors review the basics of the discrete wavelet transform (DWT) using a filter notation and introduce the SWT, where coefficient sequences are not decimated at each stage. They discuss two methods for constructing an inverse of the SWT and its potential use in nonparametric regression. The paper also develops a method for local spectral density estimation, extending standard time series concepts like the periodogram and spectrum to the wavelet context. Two practical examples from astronomy and veterinary science are presented to illustrate the effectiveness of the SWT. Additionally, the authors consider the potential of the SWT in regression and curve estimation, and its role in spectral analysis of non-stationary time series. The paper aims to provide a tutorial introduction to both the standard and SWT wavelet transforms, emphasizing their statistical applications.The paper by G.P. Nason and B.W. Silverman explores the statistical applications of wavelets, focusing on the stationary wavelet transform (SWT). The authors review the basics of the discrete wavelet transform (DWT) using a filter notation and introduce the SWT, where coefficient sequences are not decimated at each stage. They discuss two methods for constructing an inverse of the SWT and its potential use in nonparametric regression. The paper also develops a method for local spectral density estimation, extending standard time series concepts like the periodogram and spectrum to the wavelet context. Two practical examples from astronomy and veterinary science are presented to illustrate the effectiveness of the SWT. Additionally, the authors consider the potential of the SWT in regression and curve estimation, and its role in spectral analysis of non-stationary time series. The paper aims to provide a tutorial introduction to both the standard and SWT wavelet transforms, emphasizing their statistical applications.