A New Goodness-of-Fit Test for Event Forecasting and its Application to Credit Default Models
49 Pages Posted: 20 Feb 2007 Last revised: 25 Oct 2010
Date Written: August 9, 2009
Abstract
We develop a new goodness-of-fit test for validating the performance of probability forecasts. Our test statistic is particularly powerful under sparseness and dependence in the observed data. To build our test statistic, we start from a formal definition of calibrated forecasts, which we operationalize by introducing 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 robability events. After constructing test statistics for both level and shape, we provide a global goodness-of-fit statistic, which is asymptotically x^2 distributed. In a simulation exercise, we find that our approach is correctly sized and more powerful than alternative statistics. In particular, our shape statistic is significantly more powerful than the Kolmogorov-Smirnov test. Under independence our global test has significantly greater power than the popular Hosmer and Lemeshow's x^2 test. Moreover, even under dependence our global test remains correctly sized and consistent. As a timely and important empirical application of our method, we study the validation of a forecasting model for credit default events.
Keywords: Out-of-Sample Validation, Probability Calibration, Hosmer-Lemeshow Statistic, Bernoulli Mixture Models, Credit Risk
JEL Classification: C12, C52, G21
Suggested Citation: Suggested Citation
Do you have negative results from your research you’d like to share?
Recommended Papers
-
Confidence Sets for Continuous-Time Rating Transition Probabilities
-
Measurement and Estimation of Credit Migration Matrices
By Yusuf Jafry and Til Schuermann
-
Rating Transitions and Defaults Conditional on Watchlist, Outlook and Rating History
-
Credit Rating Dynamics and Markov Mixture Models
By Halina Frydman and Til Schuermann
-
Credit Rating Dynamics and Markov Mixture Models
By Halina Frydman and Til Schuermann
-
Pricing Credit Derivatives with Rating Transitions
By Viral V. Acharya, Sanjiv Ranjan Das, ...
-
Pricing Credit Derivatives with Rating Transitions
By Viral V. Acharya, Sanjiv Ranjan Das, ...
-
Pricing Credit Derivatives with Rating Transitions
By Viral V. Acharya, Sanjiv Ranjan Das, ...