This paper presents historical price data for two different crude oil types and examines the stationarity and inherent structure in oil price variation, applying many degrees of time resolution. Time Series Analysis results are then used to identify patterns and analyze the variation timescales. A specific goal of this study is to investigate and demonstrate the presence of fractal scaling. In particular, we postulate and prove that the mean size of the absolute values of price changes obeys a fractal scaling law (a power law) and can be expressed as a function of the analysis time interval (here, the latter is an independently varying parameter, ranging from a day up to a calendar year). The fractal structure of crude oil price variation is confirmed, the drift exponent is computed and the power scaling window of validity is depicted for both types, illustrating the interplay of both short- and long-term effects on the intrinsic structure of crude oil prices before and after 2008.