Financial time series analysis using the relation between MPE and MWPE

Abstract

Multi-scale permutation entropy (MPE) and multi-scale weighted permutation entropy (MWPE) are two methods to describe the complexity of systems. Compared with the former one, MWPE considers the amplitude information of time series and is a modification of MPE, so it is generally thought that MWPE is better than MPE. In this paper, we discuss the relation between the two kinds of entropy by using different simulated data, and find MPE and MWPE has a good linear correlation in the sense of multi-scale. Later, the discovery is applied to stock markets, and we confirm that it also exists in financial time series, which means that in some cases MPE can replace MWPE to study the complexity of systems without sacrificing the accuracy of time series analysis. Meanwhile, the slope of fitting line between MPE and MWPE is proposed to test nonlinearity of time series as a new discriminant statistic.