A quantity useful for nonparametric independence tests and as a complexity measure of time series

We introduce a quantity called LE-statistic. It is an easily computable functional of ordinal data with versatile applications. We demonstrate its usefulness as a statistic in a nonparametric indepen- dence test of paired samples, and as a complexity measure of a scalar time series. For chaotic orbits of one-dimensional dynamical systems it is related to the Lyapunov characteristic exponent.