Structure Parameter Optimized Kernel Based Online Prediction with a Generalized Optimization Strategy for Nonstationary Time Series

TL;DR

This paper introduces a novel online prediction method for nonstationary time series that optimizes kernel structure parameters using sparsification and covariance matrix adaptation, improving adaptability and prediction accuracy.

Contribution

It proposes a generalized optimization strategy for constructing kernel dictionaries and optimizing covariance matrices, enhancing flexibility and dynamic tracking in nonstationary time series prediction.

Findings

Superior prediction performance demonstrated in simulations

Enhanced adaptability to changing dynamics

Effective kernel structure optimization

Abstract

In this paper, sparsification techniques aided online prediction algorithms in a reproducing kernel Hilbert space are studied for nonstationary time series. The online prediction algorithms as usual consist of the selection of kernel structure parameters and the kernel weight vector updating. For structure parameters, the kernel dictionary is selected by some sparsification techniques with online selective modeling criteria, and moreover the kernel covariance matrix is intermittently optimized in the light of the covariance matrix adaptation evolution strategy (CMA-ES). Optimizing the real symmetric covariance matrix can not only improve the kernel structure's flexibility by the cross relatedness of the input variables, but also partly alleviate the prediction uncertainty caused by the kernel dictionary selection for nonstationary time series. In order to sufficiently capture the underlying dynamic characteristics in prediction-error time series, a generalized optimization strategy is designed to construct the kernel dictionary sequentially in multiple kernel connection modes. The generalized optimization strategy provides a more self-contained way to construct the entire kernel connections, which enhances the ability to adaptively track the changing dynamic characteristics. Numerical simulations have demonstrated that the proposed approach has superior prediction performance for nonstationary time series.