The L-Statistic: A Promising Functional for Real-World Data Analysis

There is a general interest in measuring the complexity of time series. It allows, e.g., to separate different states in physiological data. Some years ago we have introduced the concept of permutation entropy as a natural complexity measure which can be calculated from time series in a very simple way, a prerequisite for real-world data applications. It is related to the well-nown Kolmogorov- Sinai entropy (KSE), an important invariant of chaotic dynamical systems with a deep information-theoretical meaning. In this presentation we shortly report on these concepts, mainly from a physicist point of view. However, in the main part we present more recent results for the so-called L-statistic. It is a very fast computable functional of two ordinal time series with versatile applications, e.g., as a nonparametric statistic in the hypothesis test H0: the data are independent. However, here we first of all consider L as a complexity measure and discuss its relation to the Lyapunov exponent resp. KSE of 1D-maps.