Improved preservation of autocorrelative structure in surrogate data using an initial wavelet step

Abstract

Surrogate data generation algorithms are useful for hypothesis testing or for generating realisations of a process for data extension or modelling purposes. This paper tests a well known surrogate data generation method against a stochastic and also a hybrid wavelet-Fourier transform variant of the original algorithm. The data used for testing vary in their persistence and intermittency, and include synthetic and actual data. The hybrid wavelet-Fourier algorithm outperforms the others in its ability to match the autocorrelation function of the data, although the advantages decrease for high intermittencies and when attention is only directed towards the early part of the autocorrelation function. The improved performance is attributed to the wavelet step of the algorithm.