Surrogate Data Test on Time Series

Abstract

Given a real random-like time series, the first question to answer is whether the data carry any information over time, i.e. whether the successive samples are correlated. Using standard statistical testing, the least interesting null hypothesis of white noise has to be rejected if the analysis of the time series should be of any use at all. Further, if nonlinear methods are to be used, e.g. a sophisticated nonlinear prediction method instead of a linear autoregressive model, the null hypothesis to be rejected is that the data involve only temporal linear correlations and are otherwise random. A statistically rigorous framework for such tests is provided by the method of surrogate data. The surrogate data, generated to represent the null hypothesis, are compared to the original data under a nonlinear discriminating statistic in order to reject or approve the null hypothesis.