[Paper Review] Multifractal analysis of Chinese stocks based on partition function approach

Zhi‐Qiang Jiang, Wei‐Xing Zhou|arXiv (Cornell University)|Jan 11, 2008

Complex Systems and Time Series Analysis8 citations

TL;DR

This study applies the partition function approach to analyze multifractal properties in Chinese stock markets, examining minutely volatility across 1139 stocks and two indices. It finds significant multifractality at the 1% level, with individual stocks well modeled by a p-model with p = 0.40 ± 0.02, confirming multifractal behavior in both individual securities and the overall market through ensemble averaging.

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 $ au(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.

Motivation & Objective

• To investigate the presence and significance of multifractal properties in Chinese stock market volatility at a high temporal resolution.
• To determine whether individual stocks can be effectively modeled by a p-model derived from turbulence theory.
• To assess whether the multifractal nature observed in individual stocks extends to the overall market system through ensemble averaging techniques.

Proposed method

• The partition function approach is used to analyze scaling behavior of volatility at different box sizes s.
• Scaling exponents τ(q) are extracted from the power-law scaling of the partition function χ_q(s) with respect to s.
• Bootstrapping-based statistical tests are applied to validate the significance of the observed multifractality at the 1% level.
• The p-model is fitted to individual stocks to assess their multifractal structure, with p estimated as 0.40 ± 0.02.
• Ensemble averaging, including both quenched and annealed averages, is applied to treat each stock exchange as a single system to test for multifractal behavior at the market level.

Experimental results

Research questions

• RQ1 Does the minutely volatility of Chinese stocks exhibit significant multifractal scaling properties?
• RQ2 Can the multifractal structure of individual stocks be accurately described by the p-model with a specific p value?
• RQ3 Is the multifractal nature of individual stocks preserved and statistically significant when aggregated across the entire market via ensemble averaging?

Key findings

• The partition function χ_q(s) exhibits power-law scaling with respect to box size s, confirming the presence of scaling behavior in volatility.
• The scaling exponent τ(q) shows a nonlinear dependence on q, providing strong evidence for multifractal structure in the data.
• Statistical tests using bootstrapping confirm that the observed multifractality is significant at the 1% significance level.
• Individual stocks are well described by the p-model with a fitted parameter p = 0.40 ± 0.02, indicating a consistent multifractal structure across stocks.
• Through ensemble averaging (quenched and annealed), the study confirms that the multifractal nature persists at the market level, indicating systemic multifractality in Chinese stock markets.