Surrogate-assisted network analysis of nonlinear time series

Abstract

A recent milestone in the feld of statistical physics has been complex network theory [1]. The constituents of complex systems are translated into the nodes of a network and their interactions are represented as edges. While this procedure is straightforward for systems like social or neural networks, there is no natural way of how to create a network from a time series. In this contribution, we compare recurrence networks [2] and symbolic networks [3] to the nonlinear prediction error concerning their performance in detecting nonlinearities in time series [4]. The tests are based on surrogate data sets, uncovering the disparity of the different surrogate generating algorithms. For synthetic data of the Lorenz system, the network measures show a comparable performance. In the case of relatively short and noisy real-world data from active galactic nuclei, the nonlinear prediction error yields more robust results than the network measures. In addition, we examine the correlations in the Fourier phases of data sets from some surrogate generating algorithms. The phase correlations tend to (anti)correlate with the measures of nonlinearity and can thus be held responsible for the weak performance of the algorithms in question. These findings may further increase the knowledge of the role the Fourier phases in the field of time series analysis [5]. [1] R. Albert and A.-L. Barabasi, Rev. Mod. Phys. 74, 47 (2002) [2] R. V. Donner, Y. Zou, J. F. Donges, N. Marwan, and J. Kurths, New J. Phys. 12, 033025 (2010) [3] X. Sun, M. Small, Y. Zhao, and X. Xue, Chaos 24, 024402 (2014) [4] I. Laut and C. Räth, submitted to Phys. Rev. E. (2016) [5] C. Räath and I. Laut, Phys. Rev. E 92, 040902(R) (2015)