Analyzing the evolvement of observed time series is an important means to understand the system dynamics. Complex chaotic systems usually show the dynamical evolvement of interactional multivariate time series, so multivariate time series prediction obtains more and more attention. However, introducing redundant variables will cause a complicated prediction structure and influence the efficiency and precision of the learning algorithm, which makes it necessary to select the input variables effectively. In order to solve the problems above, this paper presents a multivariate chaotic time series prediction algorithm based on Filter and Wrapper variable selection methods to select reasonable inputs for the prediction model.Under the framework of Filter variable selection method, this paper uses Canonical Correlation Analysis (CCA) to study the relationship between variables, and presents an improved nonlinear CCA method based on Radial Basis Function (RBF) neural network and kernel function, which attempts to use a small number of variables to reflect most of the information about the original multivariate time series. To overcome the absence of a reasonable evaluation standards for Filter variable selection method, this paper presents a Wrapper variable selection method based on neural network sensitivity analysis. It uses the prediction accuracy as the evaluation criteria and defines a sensitivity function for each input node which represents the influence of the changes in input variables to the prediction output. Thus, the nodes with large sensitivity are selected as the inputs. Consider the characteristic of chaotic time series that there may exist synchronization in the phase space although they have no obvious correlation between two time series, this paper presents a nonlinear correlation analysis algorithm based on phase space synchronization. The algorithm studies the interdependence of variables in the phase space Neighborhood, and then builds a local prediction model, which shows a better evolution of multivariable chaotic time series. To test the validity of the variable selection algorithms proposed above, the algorithms are applied to the numerical simulation chaotic time series and the practical meteorological observations. Simulation results show that the methods can effectively reduce the dimension of input variables, improve the prediction accuracy and reveal the dynamics of complex systems. |