BHP Universality in Energy Sources
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We consider the α re-scaled energy source (ES) daily positive returns r(t) α and negative returns (−r(t)) α that we call, after normalization, the α positive fluctuations and α 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. Using the optimal α′s we compute analytical approximations of the probability distributions of the normalized positive and negative energy source (ES) daily returns r(t). Since the BHP probability density function appears in several other dissimilar phenomena, our results reveal a universal feature of energy source prices and a new measure that allows the comparison between the intensity of gains and losses of market activity in different energy sources prices.
KeywordsEnergy Source Probability Density Function Daily Return Positive Return Negative Return
We thank Nico Stollenwerk, Jason Gallas, Peter Holdsworth, Imre Janosi and Henrik Jensen for showing us the relevance of the Bramwell-Holdsworth-Pinton distribution. We thank Susan Jenkins for the helpful discussions and comments. A previous version of this work was presented in ICIAM 2011. We acknowledge the financial support of LIAAD-INESC TEC through ‘Strategic Project-LA 14-2013–2014’ with reference PEst-C/EEI/LA0014/2013, USP-UP project, IJUP, Faculty of Sciences, University of Porto, Calouste Gulbenkian Foundation, FEDER, POCI 2010 and COMPETE Programmes and Fundação para a Ciência e a Tecnologia (FCT) through Project “Dynamics and Applications”, with reference PTDC/MAT/121107/2010.
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