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In this paper, we perform a comprehensive entropic segmentation analysis of crude oil future prices from 1983 to 2014 which used the Jensen–Shannon divergence as the statistical distance between segments, and analyze the results from original series S and series begin at 1986 (marked as S ∗ ) to find common segments which have same boundaries. Then we apply time irreversibility analysis of each segment to divide all segments into two groups according to their asymmetry degree. Based on the temporal distribution of the common segments and high asymmetry segments, we figure out that these two types of segments appear alternately and do not overlap basically in daily group, while the common portions are also high asymmetry segments in weekly group. In addition, the temporal distribution of the common segments is fairly close to the time of crises, wars or other events, because the hit from severe events to oil price makes these common segments quite different from their adjacent segments. The common segments can be confirmed in daily group series, or weekly group series due to the large divergence between common segments and their neighbors. While the identification of high asymmetry segments is helpful to know the segments which are not affected badly by the events and can recover to steady states automatically. Finally, we rearrange the segments by merging the connected common segments or high asymmetry segments into a segment, and conjoin the connected segments which are neither common nor high asymmetric. [ABSTRACT FROM AUTHOR]

There has been considerable interest in quantifying the complexity of different time series, such as physiologic time series, traffic time series. However, these traditional approaches fail to account for the multiple time scales inherent in time series, which have yielded contradictory findings when applied to real-world datasets. Then multi-scale entropy analysis (MSE) is introduced to solve this problem which has been widely used for physiologic time series. In this paper, we first apply the MSE method to different correlated series and obtain an interesting relationship between complexity and Hurst exponent. A modified MSE method called multiscale permutation entropy analysis (MSPE) is then introduced, which replaces the sample entropy (SampEn) with permutation entropy (PE) when measuring entropy for coarse-grained series. We employ the traditional MSE method and MSPE method to investigate complexities of different traffic series, and obtain that the complexity of weekend traffic time series differs from that of the workday time series, which helps to classify the series when making predictions. [ABSTRACT FROM AUTHOR]

Multiscale entropy (MSE) is an effective method to measure the complexity of signals from complex systems, which has been applied to various fields successfully. However, MSE may yield an inaccurate estimate of entropy and induce undefined entropy as the coarse-graining procedure reduces the length of data considerably at large scales. Refined composite multiscale entropy (RCMSE) is then developed to solve this problem. However, trends superimposed in signals may significantly affect the complexity measurement. Thus we introduce an empirical mode decomposition based RCMSE, called EMD–RCMSE to first eliminate such effects of trends and then measure the complexity of signals. It is validated from simulated signals and has good estimation. In addition, this method is also applied to study the complexity of traffic signals and we obtain some interesting results: (1) Traffic signals are more complex than the results showing from RCMSE/MSE; (2) Weekday and weekend patterns (different combination of trends) greatly affect the results; (3) Complexity indices change with time at each day, due to the degree of human activities. [ABSTRACT FROM AUTHOR]