BREAK-DOWN OF SCALING AND CONVERGENCE TO GAUSSIAN DISTRIBUTION IN STOCK MARKET DATA

L. Kullmann, J. Kertész, J. Töyli, K. Kaski and A. Kanto
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L. Kullmann: Department of Theoretical Physics, Technical University of Budapest, Budafoki ut 8, H-1111, Budapest, Hungary
J. Kertész: Department of Theoretical Physics, Technical University of Budapest, Budafoki ut 8, H-1111, Budapest, Hungary;
J. Töyli: Laboratory of Computational Engineering, Helsinki University of Technology, P.O. Box 9400, FIN-02015 HUT, Finland
K. Kaski: Laboratory of Computational Engineering, Helsinki University of Technology, P.O. Box 9400, FIN-02015 HUT, Finland
A. Kanto: Department of Economics, Helsinki School of Economics and Business Administration, FIN-00100 Helsinki, Finland

International Journal of Theoretical and Applied Finance (IJTAF), 2000, vol. 03, issue 03, 371-373

Abstract: We analyze the Standard and Poor's 500 index data of the New York Stock Exchange for more than 32 years. It was suggested earlier that the high frequency data are well described by a truncated Lévy distribution and scaling with respect to the sampling time differences was found. The truncated character of the distribution implies that scaling must break down and that the distribution ultimately converges to a Gaussian. We show by comparing Lévy and Gaussian fits that the characteristic time of the break-down of scaling is of the order of few days. The analysis of the dependence of the kurtosis on the time differences shows that this is much shorter than the time needed for theconvergenceto the Gaussian being of the order of months.

Date: 2000
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DOI: 10.1142/S021902490000022X

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