Scaling and memory of intraday volatility return intervals in stock market

Fengzhong Wang; Kazuko Yamasaki; Shlomo Havlin; H. Eugene Stanley

doi:10.1103/PhysRevE.73.026117

paper

Scaling and memory of intraday volatility return intervals in stock market

arXiv:physics/0511101 · doi:10.1103/PhysRevE.73.026117

Abstract

We 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 $τ ˉ$ as $P_{q} (τ) = τ ˉ^{- 1} f (τ / τ ˉ)$ , 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.

19 pages, 8 figures

Scaling and memory of intraday volatility return intervals in stock market

Abstract

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