一种非线性相关性推断方法及其应用

Method to Test Nonlinear Dependence and Its Aplication

首先说明当观测数据量充分大时，来自于同一具有唯一紧吸引子的非线性动态系统的一维观测数据ｙ１（ｔ）或多维观测数据（ｙ１（ｔ），…，ｙｐ（ｔ））都可以用来构造对该系统分数维数的估计，且两种方法的估计结果是一致的．基于这一思想，给出了一种推断两列观测数据非线性相关性的方法，以解决非线性经济学中经济预测的变量选择问题．最后利用Ｈｅｎｏｎ映射、Ｌｏｇｉｓｔｉｃ映射仿真数据与伦敦有色金属市场镍价格实际数据说明了方法的有效性．

This paper demonstrates that when the quantity of observed data is large enough, the fractal dimension of nonlinear dynamical system with unique compact attractor can be estimated by its univariate observed time series y 1(t) or by its multivariate observed time series ( y 1(t),…,y p(t)), and the estimated results are approximately equal. According to this idea, an inference method is designed for testing nonlinear dependence between time series and can be usefully applied in variables selection for nonlinear economic forecasting. The numerical results of Henon map, Logistic map and the nickel price in LME show its effectiveness.