Universality in PSI20 fluctuations

• Type: Chapter or Part of a Book
• Date: 2011

Authors

Rui Soares Gonçalves (Author) FEUP; Helena Ferreira (Author) Other; Alberto A. Pinto (Author) FCUP

Book

Title: Dynamics, Games and Science I, DYNA 2008, in Honor of Maurício Peixoto and David Rand. Springer Proceedings in Mathematics

1º Edition

Pages: 405-420

ISBN: 978-3-642-11455-7

Publisher: Springer

Scientific classification

FOS: Natural sciences > Mathematics

Other information

Resumo (PT): We consider the α re-scaled PSI20 daily index positive returns r(t)α and negative returns ( − r(t))α called, after normalization, the α positive and negative fluctuations, respectively. We use the Kolmogorov–Smirnov statistical test as a method to find the values of α that optimize the data collapse of the histogram of the α fluctuations with the truncated Bramwell–Holdsworth–Pinton (BHP) probability density function (pdf) f { BHP} and the truncated generalized log-normal pdf f LN that best approximates the truncated BHP pdf. The optimal parameters we found are α { BHP}_+  = 0. 48, α { BHP}_−  = 0. 46, α LN  +  = 0. 50 and α LN  −  = 0. 49. Using the optimal α′s we compute analytic approximations of the probability distributions of the normalized positive and negative PSI20 index daily returns r(t). Since the BHP probability density function appears in several other dissimilar phenomena, our result reveals a universal feature of the stock exchange markets.

Abstract (EN): We consider the α re-scaled PSI20 daily index positive returns r(t)α and negative returns ( − r(t))α called, after normalization, the α positive and negative fluctuations, respectively. We use the Kolmogorov–Smirnov statistical test as a method to find the values of α that optimize the data collapse of the histogram of the α fluctuations with the truncated Bramwell–Holdsworth–Pinton (BHP) probability density function (pdf) f { BHP} and the truncated generalized log-normal pdf f LN that best approximates the truncated BHP pdf. The optimal parameters we found are α { BHP}_+  = 0. 48, α { BHP}_−  = 0. 46, α LN  +  = 0. 50 and α LN  −  = 0. 49. Using the optimal α′s we compute analytic approximations of the probability distributions of the normalized positive and negative PSI20 index daily returns r(t). Since the BHP probability density function appears in several other dissimilar phenomena, our result reveals a universal feature of the stock exchange markets.

Language: English

Type (Professor's evaluation): Scientific