The discriminant statistic based on MPE-MWPE relationship and non-uniform embedding

Abstract

The slope fitting line between MPE (multi-scale permutation entropy) and MWPE (multi-scale weighted permutation entropy) is recently proposed as a discriminant statistic for testing the nonlinearity of a time series. The main objective of this paper is to demonstrate that the selection of the optimal parameters of the non-uniform embedding is essential for the proposed discriminant statistic. In particular, the presented case studies indicate that the modified discriminant statistic based on non-uniform embedding can detect differences between such time series which remain indistinguishable if the original approach is used.