Nonlinear Mean Reversion in the Short-Term Interest Rate

Abstract

Using a new Bayesian method for the analysis of diffusion processes, this article finds that the nonlinear drift in interest rates found in a number of previous studies can be confirmed only under prior distributions that are best described as informative. The assumption of stationarity, which is common in the literature, represents a nontrivial prior belief about the shape of the drift function. This belief and the use of “flat” priors contribute strongly to the finding of nonlinear mean reversion. Implementation of an approximate Jeffreys prior results in virtually no evidence for mean reversion in interest rates unless stationarity is assumed. Finally, the article documents that nonlinear drift is primarily a feature of daily rather than monthly data, and that these data contain a transitory element that is not reflected in the volatility of longer-maturity yields.