  We describe a statistical test for association of two autocorrelated time
series, one of which generated randomly at each time point from a known but
possibly history-dependent distribution. The null hypothesis is that at each
time point, the two variables are independent, conditional on history until
that time point. We define a test statistic that is a martingale under the null
hypothesis and describe an asymptotic test for it based on the martingale
central limit theorem. If we reject this null hypothesis, we may infer an
immediate causal effect of the randomized variable on the measured variable.
