Oil Companies Share Prices Self-Affinity

The study of the variation of share prices on the stock market, as well as their behavior in the long range are not an easy task. Indeed the attempt to understand the underlying behavior on financial normally it requires a great effort because we are facing a complex system. In this work, we assess the scale properties of changes in share prices of seven oil companies listed in the NYSE stock market between the years 2008-2015 by using fractals properties. In order to do that we use the method Detrended Fluctuation Analysis (DFA), that through a power-law relation between its detrended function and $\alpha $ coefficient of correlation shows self-affinity properties in non-stationary time series. In additional we quantify the cross correlation among all seven companies by using the Detrended Cross correlation Analysis (DCCA) method, that is based on DFA. The results showed anti-persistent DFA $\alpha$ coefficient for all seven companies and the DCCA $\lambda$ coefficients were correlated among all time series. Furthermore, we use these two methods combined in order to present statistical evidence that prices oil companies variation are consistent with the Efficient Market Hypothesis (EMH). Supplementary, the $\alpha$ coefficient and $\lambda$ coefficient show that individual oil company motion cannot be predicted on long range, unless that a trader analyze the behavior motion of all companies, that avoid that individual disturb or some speculation action affect the its scale properties. The main contribution of this paper is present these scale methods (DFA and DCCA) working together in favor to help purchases and sales assets.