Bayesian Analysis of Continuous Time Models of the Australian Short Rate

This paper provides an empirical analysis of a range of alternative single-factor continuous time models for the Australian short-term interest rate. The models are indexed by the level effect parameter for the volatility in the short rate process. The inferential approach adopted is Bayesian, with estimation of the models proceeding via a Markov Chain Monte Carlo simulation scheme. Discrimination between the alternative models is based on Bayes factors, estimated from the simulation output using the Savage-Dickey density ratio. A data augmentation approach is used to improve the accuracy of the discrete time approximation of the continuous time models. An empirical investigation is conducted using weekly observations on the Australian 90 day interest rate from January 1990 to July 2000. The Bayes factors indicate that the square root diffusion model has the highest posterior probability of all the nested models.