Unit Roots and the Estimation of Interest Rate Dynamics

Clifford A. Ball and Walter N. Torous

University of California at Los Angeles, Anderson Graduate School of Management from Anderson Graduate School of Management, UCLA

Abstract: This paper investigates the time series estimation of Cox, Ingersoll, and Ross's square root, mean-reverting specification for interest rate dynamics. For a priori resonable mean reversion, the stochastic behavior of interest rates is sufficiently close to a non-stationary process with a unit root so that least squares, the generalized method of moments, as well as maximum likelihood estimation provide upward biased estimates of the model's speed of adjustment coefficient. Corresponding bond yields, as a result, exhibit excessive mean reversion. In addition, estimates of the specification's long-term mean interest rate are seen to display erratic behavior when near a unit root. These conclusions are robust to assuming multiple state variable specifications, such as Brennan and Schwartz's two factor model of interest rate dynamics. We also document conditions under which this unit root problem can be alleviated when the cross-sectional restrictions of the Cox, Ingersoll, and Ross single factor term structure model are imposed.

Date: 1992-05-18
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