基于分数维数的非线性相关度及其应用

NONLINEAR DEPENDENCE COEFFICIENT BASED ON FRACTAL DIMENSION AND ITS APPLICATIONS

首先说明利用非线性动态系统的多维观测数据和一维观测数据对系统分数维数进行估计的一致性，然后基于这一思想，给出了一种推断两列观测数据是否来自同一非线性动态系统的方法，并引入了非线性相关度的概念，以度量两列数据的非线性相关程度．该方法可用来解决非线性经济分析与预测中的变量选择问题．

In this paper it is proved that the fractal dimension estimate of nonlinear dynamical system with its multivariate observation series is the same as that with its univariate observation series.Based on this result,an inference method is presented,and the Nonlinear Dependence Coefficient is defined.This method is designed for testing nonlinear dependence between time series,and can be used in economic analysis and economic forecasting.Numerical results show that the method is effective.