LMC and SDL Complexity measures: A tool to explore time series

Abstract

This work is a generalization of the López-Ruiz, Mancini, and Calbet (LMC) and Shiner, Davison, and Landsberg (SDL) complexity measures, considering that the state of a system or process is represented by a continuous temporal series of a dynamical variable. As the two complexity measures are based on the calculation of informational entropy, an equivalent information source is defined by using partitions of the dynamical variable range. During the time intervals, the information associated with the measured dynamical variable is the seed to calculate instantaneous LMC and SDL measures. To show how the methodology works generating indicators, two examples, one concerning meteorological data and the other concerning economic data, are presented and discussed.