Different fractal properties of positive and negative returns

TL;DR

This paper investigates the fractal and multiscaling properties of positive and negative returns of the German DAX30 index, revealing significant differences in their temporal correlations and persistence during market trends.

Contribution

It is the first to analyze and compare the fractal properties of positive and negative returns separately using MFDFA, highlighting their distinct scaling behaviors.

Findings

Negative returns exhibit stronger temporal correlations than positive returns.

Both signs show multiscaling behavior in their returns.

Bear markets are more persistent than bull markets regardless of return sign.

Abstract

We perform an analysis of fractal properties of the positive and the negative changes of the German DAX30 index separately using Multifractal Detrended Fluctuation Analysis (MFDFA). By calculating the singularity spectra $f(\alpha)$ we show that returns of both signs reveal multiscaling. Curiously, these spectra display a significant difference in the scaling properties of returns with opposite sign. The negative price changes are ruled by stronger temporal correlations than the positive ones, what is manifested by larger values of the corresponding H\"{o}lder exponents. As regards the properties of dominant trends, a bear market is more persistent than the bull market irrespective of the sign of fluctuations.