An Application Study On Prediction And Analysis For Nonstationary Time Series Based On The SVM Method

A new machine learning method—support vector machine (SVM) is used tobuild forecast models on the nonstationary time series in this paper, and theapplication in weather prediction field by this method is tested and analyzed aswell. Three parts are given as follows:In the first part, the SVM regression principal and basic ideas based on thestatistical learning theory, the main idea of the forecasting model and the CMSVMsoftware are introduced systematically.In the second part, the 33 modes Lorenz system and the logistic map are used asgenerators for chaotic spatio-temporal series. We build SVM regression forecastmodels and compare them with the artificial neural network (ANN) method. Thepreliminary results are: (1) The SVM method is available for both stationary timeseries and nonstationary ones, and the correlation coefficient between the predictedvalue and the actual value can reach above 0.99. (2) The SVM regression modelsgain an advantage over the ANN method on both the forecasting accuracy and thecomputing speed, and the average relative error is about 0.3%—0.5% less than thatof the ANN method. We can consider that when we mapped a nonstationary processin the low-dimension sample space to the high-dimension (infinite-dimension)feather space by a nonlinear mapping, the nonstationarity of the system is reduced.In the third part, we use the method mentioned before to try to predict thetemperature in Miyun country in Beijing and the ozone concentration in NewDelhi. The main results are: (1) The temperature predicted value match well with theactual value and the correlation coefficient between them can reach above 0.98. Theozone concentration predicted value are a little ahead that of the actual ones and the correlation between them is 0.63. This shows that the SVM method can be used inreal data prediction. (2) With the increase of the sample numbers, the correlationcoefficient between the predicted value and the actual value are raised a bit and theprediction errors are descended obviously. That means the more informationincluded in the training sample, the more stable the model built by SVM method willbe. (3) Comparing with the SVM method, the errors produced by the ANN methodare larger when using the same temperature data to predict. It turns out that the SVMregression method also has advantages in real data prediction. (4) Both of theexamples show that there exist high errors when predicting some inflexions by SVMregression method. That maybe ascribes to the limitation of the real data and thereare little physical quality fields which have close correlation with prediction objectsin the prediction factors when training.