  We present a statistical test that can be used to verify supervisory
requirements concerning overlapping time windows for the long-term calibration
in rating systems. In a first step, we show that the long-run default rate is
approximately normally distributed with respect to random effects in default
realization. We then perform a detailed analysis of the correlation effects
caused by the overlapping time windows and solve the problem of an unknown
distribution of default probabilities for the long-run default rate. In this
context, we present several methods for a conservative calibration test that
can deal with the unknown variance in the test statistic. We present a test for
individual rating grades, and then pass to the portfolio level by suitably
adapting the test statistic. We conclude with comparative statics analysing the
effect of persisting customers and the number of customers per reference date.
