A score-test on measurement errors in rating transition times

Abstract

When modeling rating transitions as a continuous time Markov process, it is crucial to monitor the solvency of the debtors in small periodic intervals, in order to obtain suitable data for parameter estimation. If this is not done, the transition times are captured with an irregular delay, which leads to measurement errors in the transition times and consequently to biased parameter estimators. We develop a score test to check for such measurement errors in the transition data and prove the asymptotic distribution of the test statistic under the null hypothesis. The test is applied to a dataset of an international corporate portfolio of a large German bank, while accounting for economic and debtor-specific covariates. The test result is positive, indicating that measurement errors in the transition times are a real problem in practice.