1999/05/20 by Parameswaran Gopikrishnan, Vasiliki Plerou, Luis A. Nunes Amaral +2 · 4 citations
Physics and Astronomy · Economics, Econometrics and Finance · #cond-mat.stat-mech #cond-mat.dis-nn #q-fin.ST
paper · pdf · doi:10.1103/physreve.60.5305
12 pages in multicol LaTeX format with 27 postscript figures (Submitted to PRE May 20, 1999). See http://polymer.bu.edu/~amaral/Professional.html for more of our work on this area
arxiv created 1999/05/20 · arxiv updated 2009/11/30
We study the distribution of fluctuations over a time scale Δt (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 Δt, where Δt varies approximately over a factor of 104 - from 1 min up to more than 1 month. We find that the distributions for Δt ≤ 4 days (1560 mins) are consistent with a power-law asymptotic behavior, characterized by an exponent α≈ 3, well outside the stable Lévy regime 0 < α< 2. To test the robustness of the S&P result, we perform a parallel analysis on two other financial market indices. Database (iv) contains 3560 daily records of the NIKKEI index for the 14-year period 1984-97, and database (v) contains 4649 daily records of the Hang-Seng index for the 18-year period 1980-97. We find estimates of α consistent with those describing the distribution of S&P 500 daily-returns. One possible reason for the scaling of these distributions is the long persistence of the autocorrelation function of the volatility. For time scales longer than (Δt)× ≈ 4 days, our results are consistent with slow convergence to Gaussian behavior.