Multiscaling comparative analysis of time series and geophysical phenomena

Different methods are used to determine the scaling exponents associated with a time series describing a complex dynamical process, such as those observed in geophysical systems. Many of these methods are based on the numerical evaluation of the variance of a diffusion process whose step increments are generated by the data. An alternative method focuses on the direct evaluation of the scaling coefficient of the Shannon entropy of the same diffusion distribution. The combined use of these methods can efficiently distinguish between fractal Gaussian and L\'{e}vy-walk time series and help to discern between alternative underling complex dynamics.