  In this work we use numerical simulation to investigate how the temporal
length of the data affects the reliability of the estimates of brain
connectivity from EEG time--series. We assume that the neural sources follow a
stable MultiVariate AutoRegressive model, and consider three connectivity
metrics: Imaginary part of Coherency (IC), generalized Partial Directed
Coherence (gPDC) and frequency--domain Granger Causality (fGC). In order to
assess the statistical significance of the estimated values, we use the
surrogate data test by generating phase--randomized and autoregressive
surrogate data. We first consider the ideal case where we know the source time
courses exactly. Here we show how, expectedly, even exact knowledge of the
source time courses is not sufficient to provide reliable estimates of the
connectivity when the number of samples gets small; however, while gPDC and fGC
tend to provide a larger number of false positives, the IC becomes less
sensitive to the presence of connectivity. Then we proceed with more realistic
simulations, where the source time courses are estimated using eLORETA, and the
EEG signal is affected by biological noise of increasing intensity. Using the
ideal case as a reference, we show that the impact of biological noise on IC
estimates is qualitatively different from the impact on gPDC and fGC.
