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Published in:
2011 | OriginalPaper | Chapter
Universality in PSI20 fluctuations
Authors : Rui Gonçalves, Helena Ferreira, Alberto A. Pinto
Published in: Dynamics, Games and Science I
Publisher: Springer Berlin Heidelberg
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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. Using100pt]First author considered as corresponding author. Please check. 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.