A test for partial correlation between repeatedly observed nonstationary nonlinear timeseries

We describe a family of statistical tests to measure partial correlation in vectorial timeseries. The test measures whether an observed timeseries Y can be predicted from a second series X, even after accounting for a third series Z which may correlate with X. It does not make any assumptions on the nature of these timeseries, such as stationarity or linearity, but it does require that multiple statistically independent recordings of the 3 series are available. Intuitively, the test works by asking if the series Y recorded on one experiment can be better predicted from X recorded on the same experiment than on a different experiment, after accounting for the prediction from Z recorded on both experiments.