Multifractality in stock indexes: Fact or fiction?

TL;DR

This study investigates whether intraday stock indexes exhibit true multifractality and finds that observed multifractal features are likely illusions caused by data randomness rather than genuine complex scaling behaviors.

Contribution

The paper provides extensive statistical evidence that the apparent multifractality in stock indexes is not real but results from random fluctuations, challenging previous assumptions.

Findings

Mass exponent $ au(q)$ is linear across all data

Singularity $oldsymbol{ ext{α}}(q)$ is close to 1 for all days

Scaling behaviors are indistinguishable from shuffled data

Abstract

Multifractal analysis and extensive statistical tests are performed upon intraday minutely data within individual trading days for four stock market indexes (including HSI, SZSC, S&P500, and NASDAQ) to check whether the indexes (instead of the returns) possess multifractality. We find that the mass exponent $\tau(q)$ is linear and the singularity $\alpha(q)$ is close to 1 for all trading days and all indexes. Furthermore, we find strong evidence showing that the scaling behaviors of the original data sets cannot be distinguished from those of the shuffled time series. Hence, the so-called multifractality in the intraday stock market indexes is merely an illusion.