Detecting multifractal stochastic processes under heavy-tailed effects

Multifractality of a time series can be analyzed using the partition function method based on empirical moments of the process. In this paper we analyze the method when the underlying process has heavy-tailed increments. A nonlinear estimated scaling function and non-trivial spectrum are usually considered as signs of a multifractal property in the data. We show that a large class of processes can produce these effects and that this behavior can be attributed to heavy tails of the process increments. Examples are provided indicating that multifractal features considered can be reproduced by simple heavy-tailed Lévy process.