  This article proposes a systematic methodological review and objective
criticism of existing methods enabling the derivation of time-varying
Granger-causality statistics in neuroscience. The increasing interest and the
huge number of publications related to this topic calls for this systematic
review which describes the very complex methodological aspects. The capacity to
describe the causal links between signals recorded at different brain locations
during a neuroscience experiment is of primary interest for neuroscientists,
who often have very precise prior hypotheses about the relationships between
recorded brain signals that arise at a specific time and in a specific
frequency band. The ability to compute a time-varying frequency-specific
causality statistic is therefore essential. Two steps are necessary to achieve
this: the first consists of finding a statistic that can be interpreted and
that directly answers the question of interest. The second concerns the model
that underlies the causality statistic and that has this time-frequency
specific causality interpretation. In this article, we will review
Granger-causality statistics with their spectral and time-varying extensions.
