Probability flux as a method for detecting scaling

TL;DR

The paper presents a novel probability flux analysis (PFA) method for detecting scaling in time series, especially effective for heavy-tailed distributions and Levy processes, without relying on moments or binning.

Contribution

It introduces PFA as a new, efficient technique for identifying scaling in stochastic processes, independent of moments and binning procedures.

Findings

PFA effectively detects scaling in heavy-tailed distributions.

PFA outperforms diffusion entropy in certain cases.

The method is computationally efficient and robust.

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.