  Measures of the direction and strength of the interdependence between two
time series are evaluated and modified in order to reduce the bias in the
estimation of the measures, so that they give zero values when there is no
causal effect. For this, point shuffling is employed as used in the frame of
surrogate data. This correction is not specific to a particular measure and it
is implemented here on measures based on state space reconstruction and
information measures. The performance of the causality measures and their
modifications is evaluated on simulated uncoupled and coupled dynamical systems
and for different settings of embedding dimension, time series length and noise
level. The corrected measures, and particularly the suggested corrected
transfer entropy, turn out to stabilize at the zero level in the absence of
causal effect and detect correctly the direction of information flow when it is
present. The measures are also evaluated on electroencephalograms (EEG) for the
detection of the information flow in the brain of an epileptic patient. The
performance of the measures on EEG is interpreted, in view of the results from
the simulation study.
