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To investigate the relationships between the market performance of the renewable energy sector and that of the fossil fuel energy sector in Europe, this paper develops a multi-resolution analysis of the series by leveraging the tools derived from the wavelet analysis. Wavelet, by decomposing time series into their time scale components, each associated to a specific frequency range, are instrumental for studying co-movements of the fossil fuel and renewable index prices over several time horizons. The European Renewable Index, is used to describe the market price of the renewable energy sector, while the MSCI Europe Energy is designed to capture the large and mid cap companies' performance across Integrated Oil & Gas segments in Europe. The findings demonstrate the existence of areas with significant co-movements between the series at scales ranging from two-months to two-years, up to 2011. After that, areas of strong coherence are kept for a shorter amount of time, from two to six months. Moreover, despite the fact that the variables are in phase, the renewable index price is outpacing the fossil fuel price dynamic at low frequency. This relation is reversed at higher frequencies. Finally, time scale regression and nonparametric analysis suggest the cross-effects of the price series are frequency-dependent, with the indices being negatively related only in the long-run. • The relationship between fossil fuel and renewable energy prices in Europe is examined. • A multi-resolution analysis of the series is derived from the wavelet framework. • Existence of regions co-movements between the ERI and MSCI-EE prices at scales corresponding to durations. • The cross-effects of the price series are frequency-dependent. [ABSTRACT FROM AUTHOR]