The matching energy: a novel approach for measuring complexity in time series

We present the matching energy (ME) as a novel approach for nonlinear time series analysis. The time series values are first sorted by ascending and descending order. Thereafter, sequences of length n derived from the sorted and unsorted time series are compared. Finally, the ME is defined as the average of the energies of the set of sequences, where the energy of sequences with matching coordinates is set to zero. We then verified, using both simulation and experimental data, that the ME of periodic time series is equal to zero, while non-regular dynamics present a positive ME. The approach thus defined allows to scale chaos in dynamical systems and presents a high robustness against noise as well as a high-speed performance, hence is useful for real-time analysis of real-world data.