基于EEMD与DFA的Hurst指数估计

Estimation of Hurst Index Based on EEMD and DFA

去趋势波动分析(DFA)是一种研究时间序列长相关幂律特性的简单而有效的方法,其中关键的去趋势步骤就是获取序列在不同时间尺度上的局部波动函数。提出采用整体平均经验模态分解(EEMD)确定局部趋势项,去趋势操作通过移除基于EEMD的局部趋势项完成,从而给出了一种基于EEMD的DFA方法,并将其用于时间序列的Hurst指数估计。采用分形高斯噪声(FGN)和真实网络流量数据的仿真结果表明,该方法具有较好的估计效果,相比于基于EMD的DFA估计法,具有更高的估计精度。

Detrended fluctuation analysis（DFA） is a simple and very efficient method for investigating the pow- er-law long-term correlations of time series, in which a detrending step is necessary to obtain the local fluctua- tions at different timescales. Determining the local trends through ensemble empirical mode decomposition （EEMD） and performing the detrending operation by removing the EEMD-based local trends are introduced, which give an EEMD-based DFA method. The Hurst index of time series is estimated by using the proposed method. Simulation results based on fractional Gaussian noise and real network traffic data reveal that the meth- od has more efficient estimated effects. Compared with the EMD-based DFA method, the proposed method shows more accuracy.