Using wavelets for data smoothing: A simulation study

Wavelet shrinkage has been proposed as a highly adaptable approach to signal smoothing, which can produce optimum results in some senses. This paper examines the performance of the method as a function of its parameters, by simulation for time series showing gradual, rapid and discontinuous variations, for a range of signal-to-noise ratios. Some general conclusions are drawn. The effects of the choice of wavelet, choice of threshold and choice of resolution cut-off are considered. The use of the residual autocorrelation as a diagnostic tool is suggested.