Research On Univariate Nonlinear Time Series Based On Support Vector Machine

There exist a lot of univariate nonlinear time series in the fields of finance, physics,engineering and meteorology. On the one hand, nonlinear time series forecasting can helphumans control, manage and plan for the future; on the other hand, it can ensure theresources to be utilized effectively and make the revenue maximum. It is more importantthat it can help people avoid risks. Therefore, the research of nonlinear time series is ofgreat significance.The first problem to be solved is to determine the lag order of the prediction modelduring the procedure of building univariate nonlinear time series model. For chaotic timeseries, the lag order includes delay time interval and embedding dimension. At present, thestatistical methods for only determining the delay time interval include self-correlationfunction method, average mutual information method and reconstruction expansion method,etc. The statistical methods for only determining embedding dimension include testalgorithm, false near-point method and singular value decomposition method, etc. The jointmethod of determining delay time interval and embedding dimension is C-C method, etc.Unfortunately, the parameters obtained by the above methods are usually not optimalbecause determining delay time interval and embedding dimension is independent of themodel prediction. In the past years, the researchers proposed some intelligent algorithms toselect the optimal parameters for reconstructing phase space. Although these algorithmshave a certain self-adaptive, they only optimize the parameters of phase spacereconstruction or model parameters.Based on the advantages of genetic algorithm (GA) and support vector regression(SVR), in this paper, GA is used to realize the joint optimization of the lag order (the phasespace reconstruction parameters in the chaotic time series) and SVR parameters. SVR isapplied to build the prediction model. In order to demonstrate the effectiveness of theproposed method, we have conducted the experiments on four chaotic time series and two nonlinear time series. The results show that the presented method has better predictionaccuracy for univariate nonlinear time series.