Log-amplitude statistics of non-Gaussian fluctuations

Abstract

To quantify heavy-tailed distributions observed in financial time series, we propose a general method to characterize symmetric non-Gaussian distributions. 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 fluctuations of the standard deviation. Based on this framework, it is shown that statistical properties of the log-amplitude fluctuations can be estimated using the logarithmic absolute moments of the observed time series.