Kernel broad learning cauchy conjugate gradient algorithm for online chaotic time series prediction

Abstract

Accurate prediction of nonlinear systems in non-Gaussian noise environments has long been a significant challenge in the fields of statistical data analysis and time series modeling. To address this issue, this paper proposes an improved Cauchy Conjugate Gradient algorithm based on a kernel broad learning feature extraction strategy (Kernel Broad Learning Cauchy Conjugate Gradient, KBLCCG). This algorithm integrates kernel mapping with broad learning systems, forming a dual feature extraction mechanism that effectively captures the complex nonlinear structures of chaotic time series while preserving their inherent dynamic chaotic characteristics. The KBLCCG algorithm utilizes its robust feature extraction capabilities through the dual extraction mechanism of kernel mapping and broad learning systems, effectively capturing the intricate nonlinear structures present in time series data. The kernel broad learning strategy mitigates the phenomenon of kernel matrix size expansion during the iterative process, thereby reducing the computational burden and enhancing the algorithm's robustness. The Cauchy Conjugate Gradient method is employed to optimize the reduced-dimensional feature data, efficiently addressing the nonlinear prediction problem of the target sequence. Empirical analysis using simulation data and actual financial data (including the Lorenz system, Shanghai Composite Index, and CSI 300 Index) validates the performance of this method. Experimental results indicate that KBLCCG significantly outperforms existing adaptive filtering algorithms in terms of prediction accuracy, particularly demonstrating stronger generalization capabilities when dealing with complex chaotic systems. Compared to traditional methods, the kernel broad learning strategy markedly enhances the feature capturing and modeling effectiveness of chaotic time series, further validating the method's efficacy and robustness in nonlinear time series prediction. The KBLCCG algorithm not only exhibits superior predictive capabilities in complex non-Gaussian noise environments but also provides an innovative solution for handling the nonlinear and chaotic characteristics of time series prediction.