Bayesian non-linear modellings of the short term US interest rate: the help of non-parametric tools

This paper is concerned with the empirical investigation of models of the US short term interest rate, using a mixture of classical non-parametric methods and of Bayesian parametric methods. The shape of the drift and volatility functions of the usual diffusion equation are first investigated using a preliminary non-parametric analysis. The paper then develops a Bayesian method for comparing models which is based on the ability of a model to minimise the Hellinger distance between the posterior predictive density and the density of the observed sample. A discretisation of the usual diffusion equation is estimated with different parameterisations which range from variants of the constant elasticity of variance model to various switching models which draw their justifications from the preliminary non-parametric analysis. The paper concludes by some implications for the term structure. It appears that a model good at reproducing the data density is not necessarily the best for simulating the yield curve.