Traffic signals analysis using qSDiff and qHDiff with surrogate data

•We introduce a metric for complex system analysis to measure the complexity of traffic signals.•We propose and discuss a new method based on MF-DFA and surrogate data.•We investigate the multifractal behaviors of binomial multifractal series and traffic signals.•Whole week series, weekday series and weekend series are well distinguished using our method.

Complexity in time series is an intriguing feature of living dynamical systems such as traffic systems, with potential use for identification of system state. Here, we introduce a method for complex system analysis, called generalized sample entropy and surrogate data analysis, to measure the complexity in traffic signals. The behavior of the weekday series is quite different from that of the weekend series. In addition, we propose and discuss a new method of multifractality based on multifractal detrended fluctuation analysis (MF-DFA) and surrogate data. MF-DFA is the most popular method to detect multifractal characteristics of nonstationary time series. This new method is further applied to binomial multifractal series and traffic signals of Beijing, China. Results show that multifractal characteristics of the artificial data are regular and distinguishing the traffic signals of different patterns is significant. Besides, we find that there is a connection of multifractal characteristics between binomial multifractal series and traffic signals.