Detecting determinism in short time series using a quantified averaged false nearest neighbors approach

Area of Science:

• Dynamical Systems
• Time Series Analysis
• Nonlinear Dynamics

Background:

• Distinguishing deterministic chaos from stochastic processes is crucial in many scientific fields.
• Traditional methods for time series analysis often require long data sequences.
• Short time series present a significant challenge for analyzing underlying dynamics.

Purpose of the Study:

• To propose and validate a novel criterion for detecting determinism in short time series.
• To assess the effectiveness of the E2 parameter from the averaged false neighbors method for this purpose.
• To evaluate the method's robustness against noise and varying data lengths.

Main Methods:

• Estimation of the E2 parameter using the averaged false neighbors method.
• Surrogate data testing with simulated chaotic and stochastic time series.
• Analysis of the variation coefficient of E2 across different embedding dimensions (d).
• Testing with synthetic and real-world data, including the Mackey-Glass system and noisy series.

Main Results:

• The variation coefficient of E2 over embedding dimension is a suitable statistic for detecting determinism in short sequences.
• The criterion demonstrates effectiveness even for high-dimensional chaotic systems like the Mackey-Glass system.
• The method shows robustness when deterministic time series are corrupted by additive noise.
• Performance was validated across various decreasing time series lengths.

Conclusions:

• A reliable criterion for determinism detection in short time series has been established.
• The averaged false neighbors method, specifically the E2 parameter, offers a powerful tool for analyzing limited data.
• This approach enhances the capability to identify underlying deterministic dynamics in complex systems.