About the parabolic relation existing between the skewness and the kurtosis in time series of experimental data

TL;DR

This paper explores the common parabolic relationship between skewness and kurtosis in experimental time series, highlighting its general origin and potential to reveal system-specific physics.

Contribution

It demonstrates that the skewness-kurtosis parabola is a general consequence of basic constraints, while the coefficients encode physical insights about the system.

Findings

The parabolic relation is a universal feature in time series data.

Coefficients of the parabola relate to the physical properties of the system.

The analytical form of the parabola is derived from fundamental constraints.

Abstract

In this work we investigate the origin of the parabolic relation between skewness and kurtosis often encountered in the analysis of experimental time-series. We argue that the numerical values of the coefficients of the curve may provide informations about the specific physics of the system studied, whereas the analytical curve per se is a fairly general consequence of a few constraints expected to hold for most systems.