  Most of the metrics used for detecting a causal relationship among multiple
time series ignore the effects of practical measurement impairments, such as
finite sample effects, undersampling and measurement noise. It has been shown
that these effects significantly impair the performance of the underlying
causality test. In this paper, we consider the problem of sequentially
detecting the causal relationship between two time series while accounting for
these measurement impairments. In this context, we first formulate the problem
of Granger causality detection as a binary hypothesis test using the norm of
the estimates of the vector auto-regressive~(VAR) coefficients of the two time
series as the test statistic. Following this, we investigate sequential
estimation of these coefficients and formulate a sequential test for detecting
the causal relationship between two time series. Finally via detailed
simulations, we validate our derived results, and evaluate the performance of
the proposed causality detectors.
