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Universality in DAX index returns fluctuations

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  • Rui Gonc{c}alves
  • Helena Ferreira
  • Alberto Pinto

Abstract

In terms of the stock exchange returns, we compute the analytic expression of the probability distributions F{DAX,+} and F{DAX,-} of the normalized positive and negative DAX (Germany) index daily returns r(t). Furthermore, we define the alpha re-scaled DAX daily index positive returns r(t)^alpha and negative returns (-r(t))^alpha that we call, after normalization, the alpha positive fluctuations and alpha negative fluctuations. We use the Kolmogorov-Smirnov statistical test, as a method, to find the values of alpha that optimize the data collapse of the histogram of the alpha fluctuations with the Bramwell-Holdsworth-Pinton (BHP) probability density function. The optimal parameters that we found are alpha+=0.50 and alpha-=0.48. Since the BHP probability density function appears in several other dissimilar phenomena, our results reveal universality in the stock exchange markets.

Suggested Citation

  • Rui Gonc{c}alves & Helena Ferreira & Alberto Pinto, 2010. "Universality in DAX index returns fluctuations," Papers 1004.1136, arXiv.org, revised Apr 2010.
    • Handle: RePEc:arx:papers:1004.1136
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