Study On Predicting Multivariate Chaotic Time Series By Principle Component Analysis

The univariate time series obtained from the real world is always contaminated by noise and has limited length. The information provided by the univariate time series is always uncertain and incomplete. Since it is difficult to reveal the dynamics of the complex system based on the univariate time series, the predictive model sometimes is inaccurate. Multivariate time series contains much more correlative dynamic information and has a better antinoise ability. However, the multivariate time series also brings more noise and redundant information which will complex predictive model, subdue the generalization ability and results in overfitting phenomenon. In order to solve the above problems, this paper proposes a new methodology to predict multivariate chaotic time series based on principle component analysis with a view to improve estimates and predictions. The principle component analysis is applied to pretreat the input data, extract main features of multivariate time series and reduce the dimension of the model inputs. The redundant information and noise can be partly restrained. Because recurrent neural network has a feedback connection which can show the characters of the dynamic systems, recurrent neural network is used in this paper to approximate the function among the previous, current and future states of the reconstructed phase space. In order to show the main principles of chaotic multivariate time series, a improved method of principle component analysis is proposed. The method combines singular value decomposition and Hebb-based principle component analysis. It has a better convergence and stability. The method has the ability to obtain the optimal solution and trace the laggard movement. The effectiveness is shown by simulations on sunspots number and river flow multivariate time series, temperature and rainfall multivariate time series as well as a well-known multivariate chaotic benchmark system. The results show that the proposed method can reveal the dynamic characters of the complex system and enhance the accuracy of the prediction.