Multifractal analysis of Chinese stock volatilities based on partition function approach

TL;DR

This study conducts a detailed multifractal analysis of Chinese stock market volatilities using the partition function approach, revealing significant multifractal characteristics and modeling individual securities with turbulence-inspired p-models.

Contribution

It applies multifractal analysis to Chinese stock market data and confirms the multifractal nature at both individual and market levels using ensemble averaging.

Findings

Multifractal nature is statistically significant at 1% level.

Individual stocks are well modeled by the p-model with p ≈ 0.40.

Chinese stock markets exhibit multifractal characteristics at market level.

Abstract

We have performed detailed multifractal analysis on the minutely volatility of two indexes and 1139 stocks in the Chinese stock markets based on the partition function approach. The partition function $\chi_q(s)$ scales as a power law with respect to box size $s$. The scaling exponents $\tau(q)$ form a nonlinear function of $q$. Statistical tests based on bootstrapping show that the extracted multifractal nature is significant at the 1% significance level. The individual securities can be well modeled by the $p$-model in turbulence with $p = 0.40 \pm 0.02$. Based on the idea of ensemble averaging (including quenched and annealed average), we treat each stock exchange as a whole and confirm the existence of multifractal nature in the Chinese stock markets.