Surrogate-assisted network analysis of nonlinear time series

Area of Science:

• Complex systems analysis
• Time series analysis
• Astrophysical data analysis

Background:

• Detecting weak nonlinearities in time series is crucial for understanding complex systems.
• Recurrence networks and symbolic networks are methods for nonlinearity detection.
• Real-world data, such as from active galactic nuclei, are often short and noisy.

Purpose of the Study:

• To compare the performance of recurrence networks and symbolic networks against nonlinear prediction error for detecting weak nonlinearities.
• To evaluate the robustness of these methods on synthetic and real-world time series data.
• To investigate the impact of phase correlations in surrogate data on nonlinearity detection.

Main Methods:

• Utilized synthetic data from the Lorenz system.
• Applied network measures (recurrence and symbolic networks) and nonlinear prediction error.
• Employed surrogate data sets for rigorous testing.
• Examined correlations in Fourier phases of surrogate data.

Main Results:

• Network measures and nonlinear prediction error showed comparable performance on synthetic Lorenz system data.
• Nonlinear prediction error provided more robust results than network measures for short, noisy active galactic nuclei data.
• Phase correlations in surrogate data were found to influence the performance of nonlinearity detection tests.

Conclusions:

• Nonlinear prediction error offers a more reliable approach for detecting weak nonlinearities in challenging real-world time series.
• The choice of nonlinearity detection method should consider data characteristics, particularly noise and length.
• Understanding and accounting for phase correlations in surrogate data is essential for accurate nonlinearity assessment.