Multivariate multiscale sample entropy of traffic time series

Multivariate time series are common in the traffic system and are necessary for understanding the property of the traffic system. This paper introduces the multivariate multiscale sample entropy (MMSE) to evaluate the complexity in multiple data channels over different timescales. We illustrate the necessity and advantage of MMSE method by comparing MMSE results with the multiscale sample entropy results on original and shuffled traffic time series, respectively. MMSE is capable of revealing the long-range correlations and providing robust estimates for the complexity of traffic time series. Then, we utilize the MMSE to assess relative complexity of normalized multichannel temporal data in the traffic system and also reveal the weekday and weekend patterns containing in traffic signals by MMSE. MMSE can provide more accurate and helpful knowledge about the complexity of traffic time series for the dynamics and inner mechanism of traffic system from the view of multiple variables.