Scaling and memory in the return intervals of realized volatility

TL;DR

This study analyzes the scaling behavior and memory effects of return intervals of realized volatility in the Shanghai Stock Exchange, revealing improved scaling and persistent memory effects compared to traditional volatility measures.

Contribution

It demonstrates that realized volatility exhibits better scaling behavior and memory effects, with a detailed analysis across multiple stocks and the index, using high-frequency data.

Findings

Most stocks pass the KS test for scaling behavior

Return interval distributions follow a stretched exponential form

Both short-term and long-term memory effects are present

Abstract

We perform return interval analysis of 1-min {\em{realized volatility}} defined by the sum of absolute high-frequency intraday returns for the Shanghai Stock Exchange Composite Index (SSEC) and 22 constituent stocks of SSEC. The scaling behavior and memory effect of the return intervals between successive realized volatilities above a certain threshold $q$ are carefully investigated. In comparison with the volatility defined by the closest tick prices to the minute marks, the return interval distribution for the realized volatility shows a better scaling behavior since 20 stocks (out of 22 stocks) and the SSEC pass the Kolmogorov-Smirnov (KS) test and exhibit scaling behaviors, among which the scaling function for 8 stocks could be approximated well by a stretched exponential distribution revealed by the KS goodness-of-fit test under the significance level of 5%. The improved scaling behavior is further confirmed by the relation between the fitted exponent $\gamma$ and the threshold $q$. In addition, the similarity of the return interval distributions for different stocks is also observed for the realized volatility. The investigation of the conditional probability distribution and the detrended fluctuation analysis (DFA) show that both short-term and long-term memory exists in the return intervals of realized volatility.