Diagnostics and correction of systematic error while estimating transfer entropy with $K$-nearest neighbours method

Transfer entropy is widely used to detect the directed coupling in oscillatory systems from their observed time series. The systematic error is detected, while estimating transfer entropy between nonlinear systems with $K$-nearest neighbours method. The way to minimize this error is suggested: the error is decreasing with increase of the neighbour number. The possibility to detect the systematic error is shown using two sets of measured data. The achieved results make possible to rise the method sensitivity and specificity for weakly coupled nonlinear systems.