Zhi-Qiang Jiang, Wen-Jie Xie, Wei‐Xing Zhou, D. Sornette
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Multifractal analysis of financial markets: a review
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.
期刊介绍:
Reports on Progress in Physics is a highly selective journal with a mission to publish ground-breaking new research and authoritative invited reviews of the highest quality and significance across all areas of physics and related areas. Articles must be essential reading for specialists, and likely to be of broader multidisciplinary interest with the expectation for long-term scientific impact and influence on the current state and/or future direction of a field.