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Simulations of regional or global climate models are often used for climate change impact assessment. To eliminate systematic errors, which are inherent to all climate model simulations, a number of post-processing (statistical downscaling) methods have been proposed recently. In addition to basic statistical properties of simulated variables, some of these methods also consider a dependence structure between or within variables. In the present paper we assess the changes in cross-and auto-correlation structures of daily precipitation in six regional climate model simulations. In addition the effect of outliers is explored making a distinction between ordinary outliers (i.e. values exceptionally small or large) and dependence outliers (values deviating from dependence structures). It is demonstrated that correlation estimates can be strongly influenced by a few outliers even in large datasets. In turn, any statistical downscaling method relying on sample correlation can therefore provide misleading results. An exploratory procedure is proposed to detect the dependence outliers in multivariate data and to quantify their impact on correlation structures.