Scaling and Memory Effect in Volatility Return Interval of the Chinese Stock Market

TL;DR

This paper analyzes the distribution and memory effects of volatility return intervals in the Chinese stock market, revealing scaling behavior and long memory similar to other major markets.

Contribution

It demonstrates the scaling law and long memory effects in volatility return intervals specific to the Chinese stock market, expanding understanding beyond Western markets.

Findings

Scaling curve fits stretched exponential function

Evidence of clustering and memory in volatility intervals

Power-law decay in persistence probability

Abstract

We investigate the probability distribution of the volatility return intervals $\tau$ for the Chinese stock market. We rescale both the probability distribution $P_{q}(\tau)$ and the volatility return intervals $\tau$ as $P_{q}(\tau)=1/\bar{\tau} f(\tau/\bar{\tau})$ to obtain a uniform scaling curve for different threshold value $q$. The scaling curve can be well fitted by the stretched exponential function $f(x) \sim e^{-\alpha x^{\gamma}}$, which suggests memory exists in $\tau$. To demonstrate the memory effect, we investigate the conditional probability distribution $P_{q} (\tau|\tau_{0})$, the mean conditional interval $<\tau|\tau_{0}>$ and the cumulative probability distribution of the cluster size of $\tau$. The results show clear clustering effect. We further investigate the persistence probability distribution $P_{\pm}(t)$ and find that $P_{-}(t)$ decays by a power law with the exponent far different from the value 0.5 for the random walk, which further confirms long memory exists in $\tau$. The scaling and long memory effect of $\tau$ for the Chinese stock market are similar to those obtained from the United States and the Japanese financial markets.