Study Of Method On Non-stationary Time Series Prediction

Material formation process is a great complex dynamics, so the modeling by mechanism is time-consuming and difficult to ensure accuracy. In this research, by combining materials science and information technology, the evolution of external characteristics in material is considered as a non-stationary process, the dynamic model of material formation process and performance prediction of amorphous material are studied mainly.To a non-stationary time series prediction, the key is how to extract its low and high frequency components, and to avoid the over-fitted for high frequency signals. In order to solve this problem, considering the adaptability of the wavelet decomposition and the better generalization of the support vector machines for non-stationary time series, the exploratory research on the support vector machines based on statistical learning theory and the wavelet analysis with "digital microscope" reputation are adopted in this thesis. The results of test examples show the wavelet is effective tool for the non-stationary time series prediction and the least squares support vector machine can overcome some problems, such as small-sample devilishly learning, big-dimension, local minimum and slow convergent speed, in machine learning, and at the same time it have strong generalization (prediction) ability.A non-stationary time series prediction using the wavelet analysis and AR-LSSVM is proposed in this thesis. By using wavelet decomposition and reconstruction, the non-stationary time series with tendency are decomposed into a low frequency component and several high frequency components. The high frequency signals are predicted with auto-regression models, and the low frequency is predicted with least square support vector machines. The prediction result of the original time series is the superposition of the respective prediction. This new prediction method avoids the over-fitted for high frequency signals, and adequately fits the low signal of the non-stationary time series, so better predicting performance can be obtained. Experiments in the crystallization process and financial data show that the predicting method is effective.