  A long noted difficulty when assessing the reliability (or calibration) of
forecasting systems is that reliability, in general, is a hypothesis not about
a finite dimensional parameter but about an entire functional relationship. A
calibrated probability forecast for binary events for instance should equal the
conditional probability of the event given the forecast for {\em any} value of
the forecast. Attempts to estimate deviations from calibration at a specific
forecast value meet with the difficulty that the probability of the forecast
assuming that value is typically zero. Considering the estimated {\em
cumulative} deviations from reliability instead however, tests are presented
for which the asymptotic distribution of the test statistic can be established
rigorously. The distribution turns out to be universal, provided the forecasts
"look one step ahead" only, or in other words, verify at the next time step in
the future. Furthermore, the tests develop power against a wide class of
alternatives. Numerical experiments for both artificial data as well as
operational weather forecasting systems are also presented, as are possible
extensions to forecasts with longer lead times.
