Journal of Risk Model Validation

Testing retail lending models for missing cross-terms

Joseph L. Breeden


As part of the increased regulatory scrutiny of retail lending models, analysts are routinely being asked to show that their models are complete, ie, that they have captured all the structure present in the data. Rather than create increasingly complex models, we consider tests on model residuals to determine whether more structure remains to be modeled. To test for residual structure in one dimension, we discuss using the usual Durbin-Watson and Ljung-Box tests, but consider applying them along other dimensions besides calendar time. Then we expand this correlation-test concept to multiple dimensions in order to test for the presence of cross-terms in the residuals. Null hypotheses can be created by randomizing and reanalyzing the residuals. As an example, these methods are applied to the residuals of a dual-time dynamics model of US mortgage defaults. In practical applications, when residual structure is found, the analyst can then make an informed decision about whether the amount of residual structure is sufficient to warrant further modeling. Simple segmentation is often sufficient to capture the structure.

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