Scaling and memory of intraday volatility return intervals in stock market

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dc.creatorWang, Fengzhong
dc.creatorYamasaki, Kazuko
dc.creatorHavlin, Shlomo
dc.creatorStanley, H. Eugene
dc.date2005-11-11
dc.date.accessioned2026-07-07T12:07:40Z
dc.date.available2026-07-07T12:07:40Z
dc.descriptionWe study the return interval $τ$ between price volatilities that are above a certain threshold $q$ for 31 intraday datasets, including the Standard & Poor's 500 index and the 30 stocks that form the Dow Jones Industrial index. For different threshold $q$, the probability density function $P_q(τ)$ scales with the mean interval $\barτ$ as $P_q(τ)={\barτ}^{-1}f(τ/\barτ)$, similar to that found in daily volatilities. Since the intraday records have significantly more data points compared to the daily records, we could probe for much higher thresholds $q$ and still obtain good statistics. We find that the scaling function $f(x)$ is consistent for all 31 intraday datasets in various time resolutions, and the function is well approximated by the stretched exponential, $f(x)\sim e^{-a x^γ}$, with $γ=0.38\pm 0.05$ and $a=3.9\pm 0.5$, which indicates the existence of correlations. We analyze the conditional probability distribution $P_q(τ|τ_0)$ for $τ$ following a certain interval $τ_0$, and find $P_q(τ|τ_0)$ depends on $τ_0$, which demonstrates memory in intraday return intervals. Also, we find that the mean conditional interval $<τ|τ_0>$ increases with $τ_0$, consistent with the memory found for $P_q(τ|τ_0)$. Moreover, we find that return interval records have long term correlations with correlation exponents similar to that of volatility records.
dc.description19 pages, 8 figures
dc.identifierhttps://arxiv.org/abs/physics/0511101
dc.identifierhttp://arxiv.org/abs/physics/0511101
dc.identifierPhys. Rev. E 73, 026117 (2006)
dc.identifierdoi:10.1103/PhysRevE.73.026117
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/209049
dc.subjectPhysics and Society
dc.subjectStatistical Finance
dc.titleScaling and memory of intraday volatility return intervals in stock market
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