Empirically Confronting Stochastic Singularity: An Application to the Cox, Ingersoll, and Ross Model

Abstract

We just-identify a no-arbitrage term structure model in estimation and then test it using both a classical orthogonality restriction test and a test of conditional predictive ability. We treat the error structure as unmodeled heterogeneity so that the model is estimated without errors, and the statistical question is whether using the model to characterize the dynamics and patterns in historical data is either useful or optimal as a forecasting tool. The data we use are from the transparent Greenspan regime at the Fed (1989-2005), and we also use a rolling estimation format so that regime shifts are not a likely cause of the model's performance. Substantively we find that the model is not a good forecasting device for short rates which in this period are strongly affected by changes in the target Fed Funds rate. For longer term rates, especially at longer forecast horizons where Fed policy has no effect, the model is more informative.