The rise of oil prices is a main issue in contemporary economics. This study examines the monthly, weekly and daily structure in several oil prices series using a modeling approach based on fractional integration and long-range dependence. The results indicate that oil prices series are highly persistent, with orders of integration equal to or higher than 1. Breaks in the series do not alter the main conclusions of this study. That means that shocks have a permanent nature and strong policy measures must be implemented to return the series to their original long-term projections.