Volterra-MATLAB Chaotic Time Series Prediction

This MATLAB program implements one-step ahead prediction for chaotic time series using the Volterra series approach. The Volterra model is a nonlinear system modeling method that captures nonlinear system characteristics, enabling more accurate prediction of future time series values by considering higher-order nonlinear interactions. In this implementation, we first preprocess the chaotic time series data through smoothing and normalization procedures to ensure numerical stability. The algorithm then applies the Volterra series expansion, which represents the system output as a functional power series of the input. The core implementation involves estimating Volterra kernels through least squares estimation or recursive algorithms to model the nonlinear dynamics. Key MATLAB functions utilized include data preprocessing routines (smoothdata, normalize), matrix operations for kernel estimation, and optimization techniques for parameter tuning. The program structure allows users to adjust critical parameters such as series order, memory length, and regularization parameters through configurable input variables. The implementation demonstrates how Volterra models can effectively capture complex chaotic system behaviors where linear models fail. The code includes performance evaluation metrics such as prediction error analysis and convergence checks to validate model accuracy. This program serves as both a practical prediction tool and an educational resource for understanding nonlinear time series forecasting, enabling researchers to modify algorithms and extend applications to various chaotic systems. The modular design facilitates easy integration with other MATLAB toolboxes and supports further research in chaotic system analysis, parameter sensitivity studies, and comparative performance evaluations with alternative prediction methods.