Probability flux as a method for detecting scaling

Abstract

We introduce a new method for detecting scaling in time series. The method uses the properties of the probability flux for stochastic self-affine processes and is called the probability flux analysis (PFA). The advantages of this method are: 1) it is independent of the finiteness of the moments of the self-affine process; 2) it does not require a binning procedure for numerical evaluation of the the probability density function. These properties make the method particularly efficient for heavy tailed distributions in which the variance is not finite, for example, in Levy alpha-stable processes. This utility is established using a comparison with the diffusion entropy (DE) method