On the Behaviour of Weighted Permutation Entropy on Fractional Brownian Motion in the Univariate and Multivariate Setting

Abstract

The estimation of the qualitative behaviour of fractional Brownian motion is an important topic for modelling real-world applications.\xa0Permutation entropy is a well-known approach to quantify the complexity of univariate time series in a scalar-valued representation.\xa0As an extension often used for outlier detection, weighted permutation entropy takes amplitudes within time series into account.\xa0As many real-world problems deal with multivariate time series, these measures need to be extended though.\xa0First, we introduce multivariate weighted permutation entropy, which is consistent with standard multivariate extensions of permutation entropy.\xa0Second, we investigate the behaviour of weighted permutation entropy on both univariate and multivariate fractional Brownian motion and show revealing results.