A Hypothesis Test for the Long-Term Calibration in Rating Systems with Overlapping Time Windows

We present a statistical test for the long-term calibration in rating systems that can deal with overlapping time windows as required by the guidelines of the European Banking Authority (EBA), which apply to major financial institutions in the European System. In accordance with regulation, rating systems are to be calibrated and validated with respect to the long-run default rate. The consideration of one-year default rates on a quarterly basis leads to correlation effects which drastically influence the variance of the long-run default rate. In a first step, we show that the long-run default rate is approximately normally distributed. 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.