Hybrid SVMR-GPR for modeling of chaotic time series systems with noise and outliers

In this paper, the hybrid support vector machines for regression (SVMR) and Gaussian processes for regression (GPR) are proposed to deal with training data set with noise and outliers for the chaotic time series systems. In the proposed approach, there are two-stage strategies and can be a sparse approximation. In stage I, the SVMR approach is used to filter out some large noise and outliers in the training data set. Because the large noises and outliers in the training data set are almost removed, the affection of large noises and outliers is also reduced. That is, the proposed approach can be against the large noise and outliers. Hence, the proposed approach is also a robust approach. After stage I, the rest of the training data set is directly used to train the GPR in stage II. From the simulation results, the performance of the proposed approach is superior to least squares support vector machines regression (LS-SVMR), GPR, weighted LS-SVM and robust support vector regression networks when there are noise and outliers on the chaotic time-series systems.