Computing Maximum Lyapunov Exponent for Time Series Using Wolf Method

This function implements the Wolf method, a dynamic system analysis technique specifically designed for calculating the maximum Lyapunov exponent from time series data. The Wolf method serves as a powerful tool for investigating chaotic properties in dynamical systems, helping researchers understand nonlinear behaviors and their evolution over time. The implementation typically involves phase space reconstruction using time-delay embedding, followed by tracking the divergence of nearby trajectories in the reconstructed space. Key algorithmic steps include neighbor searching, divergence calculation, and exponential growth rate estimation through linear regression. The computed Lyapunov exponent quantifies the chaos level in the time series by measuring the average exponential divergence of initially close trajectories. This makes the function particularly valuable for chaos analysis in nonlinear dynamics research, with applications ranging from weather prediction to financial market analysis. The code implementation generally handles time series preprocessing, parameter optimization for embedding dimension and time delay, and robust statistical validation of the results.