Techniques for multifractal spectrum estimation in financial time series

TL;DR

This paper compares various multifractal spectrum estimation techniques, especially those based on Rénnyi entropy, applied to real financial data to assess their effectiveness in capturing data complexity.

Contribution

It provides a comparative analysis of multifractal estimation methods, highlighting the advantages of Rénnyi entropy-based approaches for financial time series.

Findings

Rénnyi entropy methods perform well with heavy-tailed data

Different techniques show varying accuracy on real financial datasets

Multifractal analysis reveals complex scaling behaviors in financial data

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.