Directed connectivity inference has become a cornerstone in neuroscience following the recent progress in imaging techniques to describe anatomical and functional networks. This paper focuses on the detection of existing connections from the observed activity in networks of 50 to 150 nodes with linear feedback in discrete time. Through the variation of multiple network parameters, our numerical results indicate that multivariate autoregressive (MVAR) estimation attains better accuracy than other standard techniques like partial correlations and Granger's causality. Based on these findings, we propose a surrogate-based significance test for connectivity detection that is shown to achieve a good control of false positive rate and to be robust to various network topology. The surrogates are generated using time rolling of the observed time series, which breaks down covariances while preserving variances: this builds a null-hypothesis distribution for each connection, from which the connectivity estimate can be compared. Our results strongly support surrogate-based MVAR estimation as a better alternative to Granger's causality test, as it properly incorporates the network feedback in the estimation model. We apply our method to multiunit activity data recorded from Utah electrode arrays in monkey to examine the detected interactions between channels for a proof of concept.