2010/04/07 by Rui Gonçalves, Gonçalves, Rui, Helena Ferreira +4 · 1 citation
Decision Sciences · Economics, Econometrics and Finance · #62P05 #91B80 #91B82 #91B84 #Complex Systems and Time Series Analysis #FOS: Economics and business #Financial Risk and Volatility Modeling #Statistical Finance (q-fin.ST) #Stock Market Forecasting Methods #msc:62P05 #msc:91B80 #msc:91B82 #msc:91B84 #q-fin.ST
paper · pdf · doi:10.48550/arxiv.1004.1136
15 pages, 12 figures
openalex publication_date 2010/04/07 · arxiv created 2010/04/12 · arxiv updated 2015/03/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In terms of the stock exchange returns, we compute the analytic expression of the probability distributions FDAX,+ and FDAX,- 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.