A Novel Hybrid Approach Combining Fractal Analysis and Machine Learning for Enhanced Prediction of Chaotic Time Series

Abstract

Predicting chaotic time series remains a significant challenge due to their inherent sensitivity to initial conditions and complex nonlinear dynamics. This paper introduces a novel hybrid approach that combines fractal analysis techniques with machine learning models to improve prediction accuracy. Specifically, we leverage fractal dimension estimation, recurrence plot analysis, and the Hurst exponent to extract key features from chaotic time series. These features are then used as inputs to a Support Vector Regression (SVR) model. The efficacy of this hybrid method is demonstrated through extensive experimentation on benchmark chaotic time series datasets, including the Lorenz attractor, Rossler attractor, and Mackey-Glass equation. Results indicate that the proposed approach significantly outperforms traditional time series prediction methods, offering a robust and accurate framework for forecasting chaotic dynamics. This hybrid strategy effectively captures both the local and global characteristics of chaotic systems, leading to enhanced predictive performance.