Multiscaling behavior in the volatility return intervals of Chinese indices

TL;DR

This paper studies the distribution and multiscaling behavior of return intervals between high-volatility events in Chinese stock indices, revealing stretched exponential forms and varying correlation exponents.

Contribution

It demonstrates multiscaling in return intervals of Chinese indices and characterizes their distribution with a stretched exponential model, providing new insights into market volatility dynamics.

Findings

Return intervals follow a stretched exponential distribution.

Multiscaling behavior is confirmed through extended self-similarity analysis.

Different thresholds q lead to different correlation exponents .

Abstract

We investigate the probability distribution of the return intervals $\tau$ between successive 1-min volatilities of two Chinese indices exceeding a certain threshold $q$. The Kolmogorov-Smirnov (KS) tests show that the two indices exhibit multiscaling behavior in the distribution of $\tau$, which follows a stretched exponential form $f_q(\tau/< \tau >)\sim e^{- a(\tau/ < \tau >)^{\gamma}}$ with different correlation exponent $\gamma$ for different threshold $q$, where $<\tau>$ is the mean return interval corresponding to a certain value of $q$. An extended self-similarity analysis of the moments provides further evidence of multiscaling in the return intervals.