多变量时间序列相空间重构的优化

基于单变量时间序列相空间重构中嵌入维数的计算常采用虚假邻点算法,但推广到多变量情形时存在多种不足,提出了一种多变量时间序列相空间重构时嵌入维数的一种改进算法。改进算法在避免使用虚假邻点算法中的判别距离和算法收敛阈值的同时,也解决了已有多变量重构算法中全局和局部较优相空间维数搜索范围的选取问题。耦合R ossler系统产生多变量时间序列的仿真计算验证了该算法的有效性。经与单变量时间序列对比试验分析,表明采用新算法重构的相空间具有较强的预测能力,由此计算得到的非线性不变量具有较高的计算精度。

Reconstructing and Optimizing Phase Space from Multivariate Time Series

An extended algorithm for reconstructing and optimizing dimensions of phase space of multivariate time series is offered,which avoids using the judging distance and convergence parameters in the False Nearest Neighbor method.Also,it can find out the optimal sub phase space dimension which is usually predefined by experience.The method is tested by coupled Rossler and the results show that the algorithm is effective.By comparing one-step ahead prediction error,maximal Lyapunov exponent and correlation dimension,reconstructed phase space by using improved method can give better predicting result and has better nonlinear characters,which is closer to the actual nonlinear dynamic system.