  Time shifting the outputs of Gravitational Wave detectors operating in
coincidence is a convenient way to estimate the background in a search for
short duration signals. However this procedure is limited as increasing
indefinitely the number of time shifts does not provide better estimates. We
show that the false alarm rate estimation error saturates with the number of
time shifts. In particular, for detectors with very different trigger rates
this error saturates at a large value. Explicit computations are done for 2
detectors, and for 3 detectors where the detection statistic relies on the
logical ``OR'' of the coincidences of the 3 couples in the network.
