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Scaling of the distribution of fluctuations of financial market indices

Parameswaran Gopikrishnan, Vasiliki Plerou, Luis A. Nunes Amaral, Martin Meyer and H. Eugene Stanley
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Parameswaran Gopikrishnan: Center for Polymer Studies, Boston University, Boston, MA
Vasiliki Plerou: Center for Polymer Studies, Boston University, Boston, MA
Luis A. Nunes Amaral: Center for Polymer Studies, Boston University, Boston, MA
Martin Meyer: Center for Polymer Studies, Boston University, Boston, MA
H. Eugene Stanley: Center for Polymer Studies, Boston University, Boston, MA

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Abstract: We study the distribution of fluctuations over a time scale $\Delta t$ (i.e., the returns) of the S&P 500 index by analyzing three distinct databases. Database (i) contains approximately 1 million records sampled at 1 min intervals for the 13-year period 1984-1996, database (ii) contains 8686 daily records for the 35-year period 1962-1996, and database (iii) contains 852 monthly records for the 71-year period 1926-1996. We compute the probability distributions of returns over a time scale $\Delta t$, where $\Delta t$ varies approximately over a factor of 10^4 - from 1 min up to more than 1 month. We find that the distributions for $\Delta t \leq$ 4 days (1560 mins) are consistent with a power-law asymptotic behavior, characterized by an exponent $\alpha \approx 3$, well outside the stable L\'evy regime $0

Date: 1999-05
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