Research On Multivariate Series Correlation Analysis And Predictive Modeling

For the multivariate time series modeling, analyzing the correlations and selecting the input variables are essential means to understand the dynamical characteristic of complex systems. As to there are not only the linear correlations but also the nonlinear correlations, the typical linear correlation analysis method plays little to the predictive modeling. Fortunately, the mutual information which is a measurement of statistical dependence in the information theory can be used to characterize the correlations of variables. In this research, the mutual information is chosen as the tool to analyze the correlation between variables, and the reasonable input variables is selected for the predictive modeling.Focusing on the problem of the smooth weights of the Averaged Shifted Histogram probability density estimation, the improved smooth weights which show the distributions more clearly are proposed to analyze the correlations based on mutual information. The input variables selection method with predictive modeling is proposed by combining the idea of stepwise regression. For another thing, focusing on the well studied sparse kernel density estimation, the kernel bandwidth is changed iteratively by minimizing the Kullbace-Leibler divergence between the true density and the estimation. The dictionary learning algorithm is introduced to reduce the data size of the training data, and a novel sparse kernel density estimation method is proposed. Therefore the mutual information correlation analysis based on the quadratic Renyi entropy is used to improve the NMIFS. However, size of the input variable set has to be determined manually. For this reason, in this paper the multi-dimensional k-nearest neighbor mutual information change ratio is proposed to determine the relevant variables and the irrelevant variables. The redundant variables are removed according to the mutual information between the input variables set. Consequently, the input variables are selected with the size of input variables determined automatically. The simulation of the synthetic data and the time series show that our methods play a well performance in the mutual information estimation and the multivariable correlation analysis, and the predictive model with high precision is build.