Hybrid multivariate time series prediction system fusing transfer entropy and local relative density

Abstract

Kernel extreme learning machine (KELM), as a natural extension of ELM to kernel learning, has been successfully applied to solve various multivariate time series prediction (MTSP) tasks. Nevertheless, the high-dimensional and nonlinear properties of prediction information against the background of big data bring great challenges to the application of KELM. Recognizing these challenges, this paper develops a KELM-based hybrid MTSP system, aiming to address the effective mining of potential relationships among variables and sample significance. Our system is initiated by devising a feature evaluation mechanism that leverages transfer entropy and directed graph theory, effectively capturing the intricate interactions and intrinsic influences among variables. Next, we introduce a robust local relative density concept to gauge the significance level of different samples in KELM learning, and develop a more efficient KELM. Diverging from previous MTSP methodologies, the developed prediction system is capable of automatically discovering potential relationships between input features and modeling, and simultaneously realizes feature subset selection and modeling learning. Empirical evidence drawn from real-world datasets substantiates the effectiveness and practicality of our proposed system. The results not only validate our approach but also highlight its theoretical and practical superiority over existing state-of-the-art methods.