Log-amplitude statistics of intermittent and non-Gaussian time series

In studies of hydrodynamic turbulence and nonequilibrium systems, it has been demonstrated that the observed non-Gaussian probability density functions are often described effectively by a superposition of Gaussian distributions with fluctuating variances. Based on this framework, we propose a general method to characterize intermittent and non-Gaussian time series. In our approach, an observed time series is assumed to be described by the multiplication of Gaussian and amplitude random variables, where the amplitude variable describes the variance fluctuation. It is shown analytically that statistical properties of the log-amplitude fluctuations can be estimated using the logarithmic-absolute moments of the observed time series. This method is applicable to a wide variety of symmetric unimodal distributions with heavy tails in order to quantify the deviation from a Gaussian distribution. By analyzing random cascade-type processes and superstatistical non-Gaussian models with power-law tails, we demonstrate that our method can provide detailed characterization in a wide range of non-Gaussian fluctuations.