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| Goodness-of-Fit Test for Event Forecasting by Andreas Blöchlinger of Zürcher Kantonalbank, and January 9, 2008 Abstract: We develop a new goodness-of-fit test for event forecasting, which builds on two components. The first component tests the level of the estimated probabilities. The second component validates the shape, measuring the differentiation between high and low probability events. We construct test statistics for both level and shape together with a global goodness-of-fit statistic, which is asymptotically 2-distributed. Since we rely on a minimal set of assumptions, our test statistics are applicable in very general settings, including situations in which forecasted events exhibit correlation and data is sparse. In a simulation exercise, we explore the reliability, power, and robustness of our approach. We illustrate the usefulness of our out-of-sample test with an empirical application, for which we focus on validating the forecasting system for credit defaults. This application is particularly suited, since defaults tend to cluster and are sparse events. JEL Classification: C12, C52, G21. Keywords: Pearson's chi-square test, Mann-Whitney-Wilcoxon U test, Receiver Operating Characteristic (ROC), Credit scoring, Basel Committee on Banking Supervision. Previously titled: Testing Probability Calibrations for Credit Scoring Models Books Referenced in this paper: (what is this?)
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