Multivariate chaotic time series analysis and prediction using improved nonlinear canonical correlation analysis

This paper proposes an improved nonlinear canonical correlation analysis algorithm named radial basis function canonical correlation analysis (RBFCCA) for multivariate chaotic time series analysis and prediction. This algorithm follows the key idea of kernel canonical correlation analysis (KCCA) method to make a nonlinear mapping of the original data sets firstly with a RBF network and a linear neural network. Then linear CCA is performed using the transformed nonlinear data sets, which corresponds to make nonlinear CCA of the original data. A modified cost function of the neural network with Lagrange multipliers and a joint learning rule based on gradient ascent algorithm which maximizes the correlation coefficient of the network outputs is used to extract the maximal correlation pattern between the input and output of a prediction model. Finally, a regression model is constructed to implement the prediction problem. The performance of RBFCCA prediction algorithm is demonstrated via the prediction problem of Lorenz time series and some practical observed time series. The results compared with the traditional neural network method and the KCCA method indicate that the RBFCCA algorithm proposed in this paper is able to capture the dynamics of complex systems and give reliable prediction accuracy.