dorsal/arxiv
View SchemaScaling and memory of intraday volatility return intervals in stock market
| Authors | Fengzhong Wang, Kazuko Yamasaki, Shlomo Havlin, H. Eugene Stanley |
|---|---|
| Categories | |
| ArXiv ID | physics/0511101 |
| URL | https://arxiv.org/abs/physics/0511101 |
| DOI | 10.1103/PhysRevE.73.026117 |
| Journal | Phys. Rev. E 73, 026117 (2006) |
Abstract
We study the return interval $\tau$ 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 $P_q(\tau)$ scales with the mean interval $\bar{\tau}$ as $P_q(\tau)={\bar{\tau}}^{-1}f(\tau/\bar{\tau})$, 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, $f(x)\sim e^{-a x^\gamma}$, with $\gamma=0.38\pm 0.05$ and $a=3.9\pm 0.5$, which indicates the existence of correlations. We analyze the conditional probability distribution $P_q(\tau|\tau_0)$ for $\tau$ following a certain interval $\tau_0$, and find $P_q(\tau|\tau_0)$ depends on $\tau_0$, which demonstrates memory in intraday return intervals. Also, we find that the mean conditional interval $<\tau|\tau_0>$ increases with $\tau_0$, consistent with the memory found for $P_q(\tau|\tau_0)$. Moreover, we find that return interval records have long term correlations with correlation exponents similar to that of volatility records.
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"abstract": "We study the return interval $\\tau$ between price volatilities that are above\na certain threshold $q$ for 31 intraday datasets, including the Standard \u0026\nPoor\u0027s 500 index and the 30 stocks that form the Dow Jones Industrial index.\nFor different threshold $q$, the probability density function $P_q(\\tau)$\nscales with the mean interval $\\bar{\\tau}$ as\n$P_q(\\tau)={\\bar{\\tau}}^{-1}f(\\tau/\\bar{\\tau})$, similar to that found in daily\nvolatilities. Since the intraday records have significantly more data points\ncompared to the daily records, we could probe for much higher thresholds $q$\nand still obtain good statistics. We find that the scaling function $f(x)$ is\nconsistent for all 31 intraday datasets in various time resolutions, and the\nfunction is well approximated by the stretched exponential, $f(x)\\sim e^{-a\nx^\\gamma}$, with $\\gamma=0.38\\pm 0.05$ and $a=3.9\\pm 0.5$, which indicates the\nexistence of correlations. We analyze the conditional probability distribution\n$P_q(\\tau|\\tau_0)$ for $\\tau$ following a certain interval $\\tau_0$, and find\n$P_q(\\tau|\\tau_0)$ depends on $\\tau_0$, which demonstrates memory in intraday\nreturn intervals. Also, we find that the mean conditional interval\n$\u003c\\tau|\\tau_0\u003e$ increases with $\\tau_0$, consistent with the memory found for\n$P_q(\\tau|\\tau_0)$. Moreover, we find that return interval records have long\nterm correlations with correlation exponents similar to that of volatility\nrecords.",
"arxiv_id": "physics/0511101",
"authors": [
"Fengzhong Wang",
"Kazuko Yamasaki",
"Shlomo Havlin",
"H. Eugene Stanley"
],
"categories": [
"physics.soc-ph",
"q-fin.ST"
],
"doi": "10.1103/PhysRevE.73.026117",
"journal_ref": "Phys. Rev. E 73, 026117 (2006)",
"title": "Scaling and memory of intraday volatility return intervals in stock market",
"url": "https://arxiv.org/abs/physics/0511101"
},
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