Structure parameter optimized kernel based online prediction with a generalized optimization strategy for nonstationary time series

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 sparsification techniques with selective online modeling criteria, and the symmetric kernel covariance matrix is intermittently optimized with the covariance matrix adaptation evolution strategy (CMA-ES). This intermittent optimization can not only improve the kernel structure's flexibility by utilizing the cross relatedness of input variables, but also partly alleviate the prediction uncertainty arisen 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 sequentially construct the kernel dictionary selection and weight vector updating procedures in multiple kernel connection modes. The generalized optimization strategy is highly flexible and effective, and it is capable of enhancing the ability to adaptively track the changing dynamic characteristics due to nonstationarity. Finally, in the perspective of top-level design, we summarize the information interaction between the network topology in kernel regressors and the optimization of inner model parameters. Numerical simulations demonstrate that the proposed approach has superior prediction performance for nonstationary time series.

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