To improve the prediction accuracy of chaotic time series, a new methodformed on the basis of local polynomial prediction is proposed. The multivariate phase spacereconstruction theory is utilized to reconstruct the p...To improve the prediction accuracy of chaotic time series, a new methodformed on the basis of local polynomial prediction is proposed. The multivariate phase spacereconstruction theory is utilized to reconstruct the phase space firstly, and on its basis, apolynomial function is applied to construct the prediction model, then the parameters of the modelaccording to the data matrix built with the embedding dimensions are estimated and a one-stepprediction value is calculated. An estimate and one-step prediction value is calculated. Finally,the mean squared root statistics are used to estimate the prediction effect. The simulation resultsobtained by the Lorenz system and the prediction results of the Shanghai composite index show thatthe local polynomial prediction errors of the multivariate chaotic time series are small and itsprediction accuracy is much higher than that of the univariate chaotic time series.展开更多
Let q be a positive integer.The graphs,called the q-trees are defined by recursion:the smallest q-tree is the complete graph K_q with q vertices,and a q-tree with n+1 vertices where n≥q is obtained by adding a new ve...Let q be a positive integer.The graphs,called the q-trees are defined by recursion:the smallest q-tree is the complete graph K_q with q vertices,and a q-tree with n+1 vertices where n≥q is obtained by adding a new vertex adjacent to each of q arbitrarily selected but mutually adjacent vertices of q-tree with n vertices.Obviously,1-trees are the graphs which are generally called trees.In this paper,it is proved that for any positive integer q,q-tree is reconstructible.展开更多
文摘To improve the prediction accuracy of chaotic time series, a new methodformed on the basis of local polynomial prediction is proposed. The multivariate phase spacereconstruction theory is utilized to reconstruct the phase space firstly, and on its basis, apolynomial function is applied to construct the prediction model, then the parameters of the modelaccording to the data matrix built with the embedding dimensions are estimated and a one-stepprediction value is calculated. An estimate and one-step prediction value is calculated. Finally,the mean squared root statistics are used to estimate the prediction effect. The simulation resultsobtained by the Lorenz system and the prediction results of the Shanghai composite index show thatthe local polynomial prediction errors of the multivariate chaotic time series are small and itsprediction accuracy is much higher than that of the univariate chaotic time series.
文摘Let q be a positive integer.The graphs,called the q-trees are defined by recursion:the smallest q-tree is the complete graph K_q with q vertices,and a q-tree with n+1 vertices where n≥q is obtained by adding a new vertex adjacent to each of q arbitrarily selected but mutually adjacent vertices of q-tree with n vertices.Obviously,1-trees are the graphs which are generally called trees.In this paper,it is proved that for any positive integer q,q-tree is reconstructible.
