Wavelet-based resampling techniques

Resampling methods were first developed in the late 1970s with the aim of obtaining estimates of the error in a statistic calculated from a sample. A necessary restriction was that the observations in the sample had to be independent, and various procedures have since been proposed to adapt the methods to dependent observations. Wavelet transforms that permit data to be analysed from a frequency or time viewpoint simultaneously have also been developed over a similar period. In simple terms, a wavelet transform produces coeffcients that are dierences between adjacent averages over increasing scales, and it has been noted that these dierences are less correlated than the original data. The potential exists, therefore, for the wavelet transform to be applied to dependent data and the resulting coeffcients, if deemed to be independent, can be resampled. Applying the inverse transform to the resampled coeffcients may produce a surrogate set of data that shares similar characteristics with the original sample.