Multifractal analysis of financial markets

TL;DR

This paper reviews the application of multifractal analysis to financial markets, highlighting its methods, evidence of multifractality, sources, and practical uses in risk management and market efficiency assessment.

Contribution

It provides a comprehensive overview of multifractal analysis methods and models applied to financial time series, and discusses their implications and open challenges.

Findings

Multifractality is widely observed in financial time series.

Multifractal analysis helps quantify market inefficiency.

It supports risk management and other financial applications.

Abstract

Multifractality is ubiquitously observed in complex natural and socioeconomic systems. Multifractal analysis provides powerful tools to understand the complex nonlinear nature of time series in diverse fields. Inspired by its striking analogy with hydrodynamic turbulence, from which the idea of multifractality originated, multifractal analysis of financial markets has bloomed, forming one of the main directions of econophysics. We review the multifractal analysis methods and multifractal models adopted in or invented for financial time series and their subtle properties, which are applicable to time series in other disciplines. We survey the cumulating evidence for the presence of multifractality in financial time series in different markets and at different time periods and discuss the sources of multifractality. The usefulness of multifractal analysis in quantifying market inefficiency, in supporting risk management and in developing other applications is presented. We finally discuss open problems and further directions of multifractal analysis.