Self-similar behaviors in the crude oil market

Abstract As the oil market has become complicated and nonlinear, the inference of similarity remains critical and challenging. In exploring the similarity between the volatility trends of different periods, the previous perspective limited to the continuous-time domain is gradually losing its advantages. We advance this issue by proposing a novel model that combines statistical and nonlinear methods to explore self-similar behaviors in the WTI crude oil market in both time and topological dimensions. Under this model, the local volatility trends are first self-adaptively distinguished as short, medium, and long-term patterns. Then, with quantifying similarities among these patterns and mapping them into the topological dimension, we find in the time domain, short-term patterns mainly cover the equilibrium periods, and the medium and long-terms mainly cover the extraordinary periods. In the topological dimension, the trends during equilibrium periods have apparent similarity relationships. However, those in unusual times are peculiar. Besides, all these patterns are grouped into ten clusters, of which nine types of self-similar behaviors and one of the extraordinary behaviors. Furthermore, based on the evolutionary features of these clusters in time domain, six particular years are identified, which can reveal the significant structural change in the oil price volatility.