Testing Arbitrage Models Without Adding an Error Model: An Application to Cox, Ingersoll, and Ross

Abstract

We demonstrate a simple procedure to test arbitrage models without adding an auxiliary error model. Our tests rely on the dynamics of the model to draw inference through out-of-sample forecasting. As an illustration, we estimate the Cox et al. model with a rolling sample to forecast zero-coupon yields from 1994 to 2007. We use these forecasts to test the model as both a candidate return generating process and to assess its efficacy as part of a forecasting method. The model is soundly rejected. Since our empirical design maintains the model's stochastic singularity, the affine term structure model's poor empirical performance cannot be blamed on an unfortunate choice of an auxiliary error model. Unlike earlier studies, the traditional expectations hypothesis holds in our sample, and the model cannot reproduce this feature of the data.