  We consider the problem of detecting causal relationships between discrete
time series, in the presence of potential confounders. A hypothesis test is
introduced for identifying the temporally causal influence of $(x_n)$ on
$(y_n)$, causally conditioned on a possibly confounding third time series
$(z_n)$. Under natural Markovian modeling assumptions, it is shown that the
null hypothesis, corresponding to the absence of temporally causal influence,
is equivalent to the underlying `causal conditional directed information rate'
being equal to zero. The plug-in estimator for this functional is identified
with the log-likelihood ratio test statistic for the desired test. This
statistic is shown to be asymptotically normal under the alternative hypothesis
and asymptotically $\chi^2$ distributed under the null, facilitating the
computation of $p$-values when used on empirical data. The effectiveness of the
resulting hypothesis test is illustrated on simulated data, validating the
underlying theory. The test is also employed in the analysis of spike train
data recorded from neurons in the V4 and FEF brain regions of behaving animals
during a visual attention task. There, the test results are seen to identify
interesting and biologically relevant information.
