The problem of the definition and evaluation of brain connectivity has become a central one in neuroscience during the latest years, as a way to understand the organization and interaction of cortical areas during the execution of cognitive or motor tasks. The method of the directed transfer function (DTF) is a frequency-domain approach to this problem, based on a multivariate autoregressive modeling of time series and on the concept of Granger causality. So far, all the connectivity estimations performed on cerebral electromagnetic signals were computed between signals gathered from the electric or magnetic sensors. However, the spreading of the potential from the cortex to the sensors makes it difficult to infer the relation between the spatial patterns on the sensor space and those on the cortical sites. In this paper we propose the use of the DTF method on cortical signals estimated from high resolution EEG recordings, which exhibit a higher spatial resolution than conventional cerebral electromagnetic measures. As main contributions of this work, we present the results of a wide simulation study, aiming to evaluate performances of DTF application on this kind of data, and a statistical analysis (via the ANOVA, analysis of variance) of the results obtained for different levels of signal to noise ratio and temporal length, as they have been systematically imposed on simulated signals. Finally, we provide an application to the estimation of cortical connectivity from high resolution EEG recordings related to finger tapping movements.