Techniques for multifractal spectrum estimation in financial time series

Abstract

Multifractal analysis is one of the important approaches that enables us to measure the complexity of various data via the scaling properties. We compare the most common techniques used for multifractal exponents estimation from both theoretical and practical point of view. Particularly, we discuss the methods based on estimation of R\'enyi entropy, which provide a powerful tool especially in presence of heavy-tailed data. To put some flesh on bare bones, all methods are compared on various real financial datasets, including daily and high-frequency data.