On the Behaviour of Permutation Entropy on Fractional Brownian Motion in a Multivariate Setting

The investigation of qualitative behaviour of the fractional Brownian motion is an important topic for modelling theoretic and real-world applications. Permutation Entropy is a robust and fast approach to quantify the complexity of a time series in a scalar-valued representation. There are numerous studies on the behaviour of Permutation Entropy on fractional Brownian motion. Similarly, Multi-Scale Permutation Entropy is used to study structures on different time scales in a univariate context. Nevertheless, many real-world problems contain multivariate time series. In this paper we investigate the behaviour of Permutation Entropy as well as the behaviour of Multi-Scale Permutation Entropy on fractional Brownian motion - each in the multivariate case. We show that the multivariate results are consistent with known univariate results.