探测交通时间序列长相关性的多重分形消除趋势波动分析方法

Detecting Long-range Correlations of Traffic Time Series with Multifractal Detrended Fluctuation Analysis

交通时间序列的多重分形性通常与交通流时间序列的长相关性或概率密度函数有关。本文应用多重分形消除趋势波动分析(MF-DFA)方法来研究交通流时间序列。通过分析北京玉泉营快速路的速度时间序列,我们发现速度时间序列存在一个时间标度值,其前后的信号分别具有不同的相关指数。最后,我们用MF-DFA方法对原始序列和扰动序列进行分析比较,发现交通时间序列的多重分形性主要是由交通流的相关性决定的。

Multifractal behavior in traffic time series usually connected with different long-range (time-) correlations of the small and large fluctuations or (and) a broad probability density function for the values of the time series. Multifractal detrended fluctuation analysis (MF-DFA) is used to study the traffic speed fluctuations. It is demonstrated that the speed time series, observed on the Beijing Yuquanying highway over a period of about 40 months, has a crossover time scale sx , where the signal has different correlation exponents in time scales s >sx and s<sx. Finally, the long-range correlation was validated to be dominant by the method of comparing the MFDFA results for original series to those obtained via the MFDFA for shuffled series.