Wavelet-based surrogates for testing time series

Thieler et al. (1992) introduced the notion of generating `surrogate´ time series as a way of testing for nonlinearities in a time series of interest against a null hypothesis that the series is a realization of a stationary Gaussian process. This idea of surrogate time series is very close to the notion of `bootstrapping´ time series. Both methods attempt to approximate the unknown distribution for a test statistic under the null hypothesis by generating time series that can be taken to be additional realizations of the Gaussian stationary process from which the given time series is assumed to come. Thieler proposed generating the surrogate series via the frequency domain by manipulating the discrete Fourier transform (DFT) for the observed series. Here we consider an alternative approach based upon the discrete wavelet transform (DWT)