  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.
