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

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.

10 elsart pages including 7 eps figures

References in corpus (6)

• Empirical distributions of Chinese stock returns at different microscopic timescales
• Indication of multiscaling in the volatility return intervals of stock markets
• Inverse cubic law of index fluctuation distribution in Indian markets
• Quantifying bid-ask spreads in the Chinese stock market using limit-order book data: Intraday pattern, probability distribution, long memory, and multifractal nature
• Volatility return intervals analysis of the Japanese market
• Empirical regularities of order placement in the Chinese stock market

Cited by in corpus (7)

• Statistical properties of volatility return intervals of Chinese stocks
• Multiscaling behavior in the volatility return intervals of Chinese indices
• Scaling and memory in the return intervals of realized volatility
• Recurrence interval analysis of trading volumes
• Scaling and memory in the return intervals of energy dissipation rate in three-dimensional fully developed turbulence
• Empirical properties of inter-cancellation durations in the Chinese stock market
• Analysis of inter-transaction time fluctuations in the cryptocurrency market