Prediction of multivariate time series based on principal component analysis and neural networks
Min Han · Control theory & applications · 2007
Most of previously published prediction methods are concentrated on the modeling of univariate time series.The main purpose of this paper is to study a new methodology to model and predict multivariate nonlinear time series.Firstly,both the linear correlations and the nonlinear correlations are detected to initialize an embedding delay window,which could contain enough information for prediction.Then,the principal components analysis(PCA) method is expanded to extract the joint information of multiple variables in a complex system since PCA could find the uncorrelated directions of maximum variance in the data space of different variables.The multivariate phase space is reconstructed.Furthermore,neural network makes predictions on the basis of approximating both the functional relation between different variables and the map between current state and future state.Finally,two simulation examples,one is from the typical Ro¨ssler equation and the other is from the practically observed values of rainfall and temperature of Dalian,are used to explain the validity of the proposed method.It provides a new way to analyze the multivariate time series.