Comment on ‘multifractal diffusion entropy analysis on stock volatility in financial markets’ [Physica A 391 (2012) 5739–5745]

In their recent article ‘multifractal diffusion entropy analysis on stock volatility in financial markets’ Huang, Shang and Zhao (2012) [6] suggested a generalization of the diffusion entropy analysis method with the main goal of being able to reveal scaling exponents for multifractal times series. The main idea seems to be replacing the Shannon entropy by the Rényi entropy, which is a one-parametric family of entropies. The authors claim that based on their method they are able to separate long range and short correlations of financial market multifractal time series. In this comment I show that the suggested new method does not bring much valuable information in obtaining the correct scaling for a multifractal/mono-fractal process beyond the original diffusion entropy analysis method. I also argue that the mathematical properties of the multifractal diffusion entropy analysis should be carefully explored to avoid possible numerical artefacts when implementing the method in analysis of real sequences of data.

Huang, Shang and Zhao suggested a generalization of the diffusion entropy analysis.
► The authors claim that they are able to separate long range and short correlations of multifractal time series.
► I show that the new method does not bring valuable information beyond the original diffusion entropy analysis.
► Mathematical properties of the new method should be carefully explored to avoid possible numerical artefacts.