Computing the Largest Lyapunov Exponent for Time Series Using Wolf's Method

This function computes the largest Lyapunov exponent for time series data, which serves as a key indicator for quantifying chaos in dynamical systems. The Wolf method represents a widely-used algorithm for Lyapunov exponent calculation. To ensure accurate computation, the function requires input of both the raw time series data and relevant parameters characterizing the time series structure. Specifically, essential inputs include the time series length, embedding dimension (for phase space reconstruction), and time delay parameter (tau). The implementation follows Wolf's original approach by tracking the divergence of nearby trajectories in reconstructed phase space. Key algorithmic steps involve: phase space reconstruction using time-delay embedding, nearest neighbor identification, divergence tracking with periodic renormalization, and linear regression to estimate the exponent from divergence rates. It's critical to note that parameter selection requires careful consideration of inter-parameter dependencies, as improper embedding dimension or time delay values may compromise result accuracy. The function automatically handles trajectory normalization and includes safeguards against poor neighbor selection.