The simultaneous occurrences of events in two binary time series may be attributed to simple chance or else may imply a substantive link between the sources of the two series. Bernoulli models can test the null hypothesis of chance coincidence when data are i.i.d. Logistic models can account for more complex binary time series having autocorrelation, trend and seasonality. However, when investigating multiple series for possible connections, even stringent tests can uncover a huge number of apparent relationships for investigation. In these cases, attention must be paid to the false discovery rate to avoid wasting time on false target pairs.