Detecting long-range correlations of traffic time series with multifractal detrended fluctuation analysis

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 (MFDFA) 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.