Modern portfolio theory advises investors to diversify their assets to reduce risk. Diversification encompasses two major concepts: international and temporal diversifications. While international diversification tells investors how many and what type of assets they should put in their portfolios to diversify them, temporal diversification tells them how long they should hold the assets in their portfolios. To investigate these questions simultaneously, we propose an alternative approach based on two recent methodologies: wavelets and copulas. We focus on seven stock market indexes in different geographical areas. Our main findings are the following. First, we confirm the usual benefits of international diversification. Second, the results of nonparametric copulas show that the shape of the copula varies across the long or short term of the relationship. Third, this methodology shows some structural differences in dependencies across different timescales. We then highlight the existence of potential holding periods that allow investors to improve their diversification processes and identify risks.