Failure of pseudo-periodic surrogates

Abstract

A surrogate test is a method for determining the properties of time-series data. Some methods have been proposed to generate surrogate data that can be used to determine whether a pseudo-periodic time series has deterministic properties beyond pseudo-periodicity. Luo’s method is one such method. In this article, Luo’s method and the problems associated with it are discussed. In this method, surrogate datasets are produced by adding the time-shifted data to the original data. Consequently, the pseudo-periodicity of the time series is presumably preserved, but the fine structure related to the deterministic properties is destroyed. Luo’s method gives correct results for many data. However, it generates incorrect results for certain time series, for example, the time series of the Rössler chaotic attractor and phase-shifted sinusoidal waves. To overcome this problem, we propose an alternative method based on the Poincaré section.