A wavelet-based method for surrogate data generation

Hypothesis testing based on surrogate data has emerged as a popular way to test the null hypothesis that a signal is a realisation of a linear Gaussian, stochastic process. If these surrogates are constrained to the values and power spectrum of the original data there is no need to formulate a pivotal test statistic. In this paper a method is presented for generating constrained surrogates using a wavelet transform, introducing a threshold above which wavelet detail coefficients are pinned to their original values. Such surrogates avoid problems of nonstationarity for pseudo-periodic data and appear to be more robust than conventional approaches for situations where period modulation is corrupting a Gaussian stochastic process. When used for generating ensemble realisations of a process, the approach used here avoids some of the difficulties of methods based on simple randomisation of wavelet coefficients.