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 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.