Weighted multivariate composite multiscale sample entropy analysis for the complexity of nonlinear times series

Abstract

Multivariate multiscale sample entropy (MMSE) has recently been proposed to evaluate complexity of time series. However, the results of estimation of complexity by MMSE method may be inaccurate as the coarse-graining procedure reduces the length of the time series at a large scale. In addition, MMSE has some limitations, mainly its inability to detect abrupt changes in the signal and ignore the difference between distinct patterns. In order to overcome those above limitations of MMSE, this paper introduces the weighted multivariate composite multiscale sample entropy (WMCMSE) as a measure to characterize the complexity of nonlinear time series. And we illustrate the necessity of WMCMSE method by comparing WMCMSE results with multivariate multiscale sample entropy (MMSE), weighted multivariate multiscale sample entropy (WMMSE), multivariate composite multiscale sample entropy (MCMSE) on random series. Then, WMCMSE method is employed to study the complexity of traffic speed and volume time series of Beijing Ring 2, 3, 4 roads, which are from August 11th to October 20th, 2012. The results of WMCMSE show that the WMCMSE method can distinguish the behavior of the flow time series, which means that we can detect the congested traffic system. We found that road condition of ring 2, 3, 4 road is very different. Compared to the ring 4 road, the values of the WMCMSE of the ring 2 and 3 roads are higher, indicating that the traffic flow on Ring 2 and Ring 3 road are more complex compared to Ring 4 road. The higher the complexity, the more traffic jams. Government departments can judge the traffic congestion of that time period and that road according to the complexity differences between different time periods and different roads, and then take different measures.