Research On Nonlinear Time Series Prediction Based On Support Vector Machine

As the main technique of the quantitative forecast, the method of time series prediction is used almost in all fields of forecast. The traditional methods of time series prediction mainly focus on linear time series and weak nonlinear time series, so they lack effectiveness when they face complex nonlinear time series (even chaos time series). Support Vector Machine (SVM) is a kind of novel machine learning methods, theoretically based on statistic learning theory. It employs the criteria of structural risk minimization and provides a framework for the small samples, nonlinearity and high dimension problems. SVM has been applied in nonlinear time series prediction in recent years. Focusing on raising accuracy of SVM prediction model, this paper studies noise-reduction, non-stationary processing and model parameters optimization of nonlinear time series.Although widely applied in nonlinear time series analysis, the noise reduction method via local projection has the subjectivity of selecting the neighborhood, which greatly affects the performance. A new method by local projection using adaptive neighborhood selection is studied. First, one dimensional time series are embedded into a high dimensional phase space according to time-delay theory. The neighborhood size for each candidate phase point in phase space is increased by adding neighboring point one by one. The optimal neighborhood size for the phase point is determined during the direction's variation of the most significant eigenvector of neighborhood as size increasing, and then the noise is eliminated through local geometric projection. Experiment results show that adaptive neighborhood selection can improve the noise reduction performance of local projection method.Non-stationary time series has periodicity and randomness so that it is difficult to construct the model of accurate forecast with single method. A hybrid forecasting method based on Empirical Mode Decomposition (EMD) and Least Square Support Vector Machine (LS-SVM) is presented in this paper. Firstly, the non-stationary time series is adaptively decomposed into a series of stationary intrinsic mode functions (IMF) in different scale space using EMD. Then the right parameter and kernel functions are chosen to build different LS-SVM respectively to every IMF. Finally, these forecasting results of each IMF are combined to obtain final forecasting result. This method is successfully applied to non-stationary trend prediction of mechanical vibration.Phase space reconstruction and SVM parameters optimization are two important aspects for improving prediction performance and are solved separately traditionally. This paper proposes a joint optimization algorithm based on Hybrid PSO. This method combines the discrete PSO with the continuous-valued PSO to simultaneously optimize the phase space reconstruction and the SVM parameters setting. The experimental results showed the proposed approach can raise prediction accuracy.