除趋势交叉波动分析函数的统计特征

Statistical Properties of Detrended Cross-Correlation Analysis

除趋势波动分析(DFA)是测量非平稳时间序列相关性的方法之一,对DFA方法适当改进,可推广到在二维时间序列中研究数据之间的交叉相关性.为了得到这种改进方法与DFA方法之间的数量关系,本文分别就两列时间序列具有线性相关性与不具有线性相关性的情况进行讨论,并对它们的交叉相关指数与DFA指数之间的关系进行分析.最后,用改进方法对交通时间序列进行研究,结果表明:交通速度与交通流量数据之间具有较强的交叉相关性.

Detrended fluctuation analysis（DFA）is a method for analyzing the long-range dependence non-stationary time series.This paper modifies the DFA method to two dimension for considering the cross-correlation properties.In order to investigate the relation between DFA method and the modified method,this paper analyzes the dependence property of cross-correlation exponent on DFA exponent for linear correlation and nonlinear correlation data,respectively.Furthermore,the modified method is applied to traffic time series and the cross-correlation is found in traffic flow and volume data.