Multiscale multifractal detrended cross-correlation analysis of traffic flow

Abstract

In this paper, we introduce a method called multiscale multifractal detrended cross-correlation analysis (MM-DCCA) to describe the cross-correlation properties depend on the timescale in which the multifractality is computed. For traffic time series, we show that the fractal properties of cross-correlations have a relationship with the range of scale indicating the great necessity to study the cross-correlation properties between two time series at multiple scales. MM-DCCA gains a new insight into measuring different fractal properties of the cross-correlations between traffic series by sweeping all the range of scale, and it provides much richer information than multifractal detrended cross-correlation analysis (MF-DCCA). The Hurst surfaces present multifractal properties and strong long-range persistent cross-correlations between traffic series. By comparing Hurst surfaces before and after removing dominant periodicities, we find that periodicity is not the only reason which causes the crossover and dominates the cross-correlation. There are other interesting factors or underlying traffic mechanisms containing in the cross-correlation between traffic series. Moreover, the cross-correlation between the whole traffic series can be considered as a combination of both weekday and weekend parts. The results also suggest that the different periodic patterns hidden in the weekday and weekend patterns are the main distinction between them and play an important role in the Hurst surface of cross-correlation investigation.