MATLAB Implementation of Volterra Adaptive Prediction for Time Series Analysis

This MATLAB program implements Volterra adaptive prediction for testing adaptive prediction capabilities and reconstructing phase space from chaotic sequences. Volterra adaptive prediction is a nonlinear system-based forecasting method that analyzes historical system data and input signals to predict future system behavior. The program employs Volterra series expansion with adaptive filter coefficients updated using LMS or RLS algorithms to handle nonlinear dynamics. For phase space reconstruction, the code implements time-delay embedding methods (using functions like delay embedding and false nearest neighbors analysis) to transform chaotic time series into point sets in phase space, enabling better understanding of chaotic system dynamics. Key functions include: nonlinearVolterraFilter() for adaptive prediction, phaseSpaceReconstruct() for embedding dimension optimization, and chaosAnalysis() for Lyapunov exponent calculation. This implementation helps researchers study characteristics of chaotic sequences and nonlinear systems through practical MATLAB simulations. The program includes example datasets and visualization tools for result analysis. We hope this program proves valuable for your nonlinear time series research!