Permutation and weighted-permutation entropy analysis for the complexity of nonlinear time series

• A multiscale weighted-permutation entropy (MSWPE) is applied to traffic series.
• We detect the temporal structures and investigate complexity of traffic signals.
• MSWPE can distinguish the differences between workday and weekend time series clearly.

Permutation entropy (PE) has been recently suggested as a relative measure of complexity in nonlinear systems, such as traffic system and physiology system. A weighted-permutation entropy (WPE) analysis based on the weight assigned to each vector was proposed to consider the amplitude information. We introduce PE/WPE technique to multiple time scales, called multiscale permutation entropy (MSPE)/multiscale weighted-permutation entropy (MSWPE), which are applied to investigate complexities of different traffic series. Both approaches successfully detect the temporal structures of traffic signals and distinguish the differences between workday and weekend time series.