Solving Nonlinear System Time Series Prediction Problems Using Statistical Chaos Methods

In this article, we demonstrate how to use MATLAB to address nonlinear system time series prediction problems. Specifically, we explore the application of statistical chaos methods for forecasting such time series. Statistical chaos methodology represents an analytical approach grounded in chaos theory, which enables the investigation of complex dynamic behaviors in nonlinear systems. We provide a detailed implementation guide for this method in MATLAB, including key functions such as phase space reconstruction using the delay function, Lyapunov exponent calculation via lyapunovExponent algorithms, and chaos characteristic analysis through correlationDimension computations. Practical examples illustrate the application of these techniques to real-world problems, complete with code snippets demonstrating time series embedding and prediction model implementation. Additionally, we discuss the method's advantages in capturing nonlinear dynamics and its limitations regarding data requirements and computational complexity. The article concludes with suggestions for future research directions, including potential enhancements to the prediction algorithms and optimization techniques for handling larger datasets.