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Scaling and memory of intraday volatility return intervals in stock markets.
MedLine Citation:
PMID:  16605408     Owner:  NLM     Status:  PubMed-not-MEDLINE    
Abstract/OtherAbstract:
We study the return interval tau between price volatilities that are above a certain threshold q for 31 intraday data sets, including the Standard and Poor's 500 index and the 30 stocks that form the Dow Jones Industrial index. For different threshold q, the probability density function Pq(tau)scales with the mean interval tau as [Formula: see text], 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 and still obtain good statistics. We find that the scaling function f(x)is consistent for all 31 intraday data sets in various time resolutions, and the function is well-approximated by the stretched exponential, f(x) similar to e(-ax)(gamma), with gamma=0.38+/-0.05 and a=3.9+/-0.5, which indicates the existence of correlations. We analyze the conditional probability distribution Pq(tau/tau0) for tau following a certain interval tau0, and find Pq(tau/tau0) depends on tau0, which demonstrates memory in intraday return intervals. Also, we find that the mean conditional interval (tau/tau0) increases with tau0, consistent with the memory found for Pq(tau/tau0). Moreover, we find that return interval records, in addition to having short-term correlations as demonstrated by Pq(tau/tau0), have long-term correlations with correlation exponents similar to that of volatility records.
Authors:
Fengzhong Wang; Kazuko Yamasaki; Shlomo Havlin; H Eugene Stanley
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Publication Detail:
Type:  Journal Article     Date:  2006-02-16
Journal Detail:
Title:  Physical review. E, Statistical, nonlinear, and soft matter physics     Volume:  73     ISSN:  1539-3755     ISO Abbreviation:  Phys Rev E Stat Nonlin Soft Matter Phys     Publication Date:  2006 Feb 
Date Detail:
Created Date:  2006-04-11     Completed Date:  2006-06-20     Revised Date:  -    
Medline Journal Info:
Nlm Unique ID:  101136452     Medline TA:  Phys Rev E Stat Nonlin Soft Matter Phys     Country:  United States    
Other Details:
Languages:  eng     Pagination:  026117     Citation Subset:  -    
Affiliation:
Center for Polymer Studies and Department of Physics, Boston University, Boston, MA 02215, USA.
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