**2. Methodology**

Our hypothesis test aims to identify multifractal scaling in the presence of heavy tails. It is constructed based on the different distributions of concavity measures for various tail indices:

> *H*0: The process of interest is not multifractal. vs. *HA*: The process of interest is multifractal.

In this section, we first introduce the measure of concavity and tail index implemented in this paper. Then, we examine the distributions of concavity measures with regard to various tail indices for different processes. The following four instances are chosen: monofractal process (Brownian motion and fractional Brownian motion); Student *t*-distributed processes with degrees of freedom between 1 and 20; and a multifractal process simulated using BMMT with a log-Normal multiplicative measure.
