The goal of this study is to assess the strength and mode of price dependence by time scale, among the extra virgin olive oil markets of Italy, Spain, and Greece. These three Mediterranean countries are responsible for 95% of olive oil production within the European Union and they account for more than 50% of the olive oil exports worldwide. For the empirical analysis, monthly prices from the aforementioned countries are utilized along with the tools of discrete wavelets and non-parametric copulas. Results indicate that (a) price linkages in the short run are significantly different from those in the longer run, with price dependence being stronger in the longer run, and (b) in the very long run, price shocks of the same sign but of different magnitude are transmitted from Italy to Spain with a higher probability than they are transmitted from Italy to Greece. Accordingly, the time scale affects the intensity as well as the pattern of dependence, pointing this way to asymmetric price co-movement. Regarding the integration of the three markets, the finding of asymmetric co-movement is not consistent with well-integrated markets.