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

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 information 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.