Detecting the Type of Multi-Fractality in Traffic Time Series

Abstract

In general, two types of multi-fractality can be identified in time series. One type connects with a broad probability density function for the values of the time series, while the other connects with different long-range correlations of the small and large fluctuations. Recent analyses of traffic time series indicate that it exhibits multi-fractal properties. But which type of multi-fractality does it exhibit? In this paper, multi-fractal detrended fluctuation analysis (MF-DFA) is used to study traffic speed fluctuations. Collected data shows that the speed time series, observed by microwave detector system on the outer side of the North Second Ring Road over a period of about 60 days, has strong multi-fractal properties. By comparing the fluctuation function of MF-DFA results for the original series to those for shuffled series, we find that the type of multi-fractality in traffic speed time series is consistent with long range correlations of the small and large fluctuations. In addition, by comparing the generalized Hurst exponent and multi-fractal spectrum of the original time series with those of the corresponding shuffled series, the results show that the multi-fractal properties of shuffled time series are stronger than those of the original time series, and both distribution multi-fractality and correlation multi-fractality are present in the speed time series.