Surrogate-assisted network analysis of nonlinear time series

TL;DR

This paper compares the effectiveness of recurrence and symbolic networks versus nonlinear prediction error in detecting weak nonlinearities in time series, highlighting their relative robustness and the influence of surrogate data phase correlations.

Contribution

It provides a comparative analysis of network-based methods and nonlinear prediction error for nonlinearity detection, including the impact of surrogate data phase correlations.

Findings

Network measures perform similarly to nonlinear prediction error on Lorenz data.

Prediction error is more robust on short, noisy real-world data.

Phase correlations in surrogate data affect nonlinearity test performance.

Abstract

The performance of recurrence networks and symbolic networks to detect weak nonlinearities in time series is compared to the nonlinear prediction error. For the 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. The tests are based on surrogate data sets. The correlations in the Fourier phases of data sets from some surrogate generating algorithms are also examined. The phase correlations are shown to have an impact on the performance of the tests for nonlinearity.