Abstract: The Cox-Ingersoll-Ross model (CIR) is a diffusion process with widespread applications in economics, finance and population biology. In this paper we first obtain a full Gibbs Sampler for the exact CIR process observed at equidistant times. We do not require the imposition of the Feller condition. We show how to carry out smoothing and handling of missing data. Additionally, the introduction of a tailored single Metropolis-Hastings step allows us to handle irregular and random time intervals. Secondly, we obtain several asymptotic properties which include Local Asymptotic Normality, consistency and asymptotic normality of conditional maximum likelihood estimation and a Bernstein-von Mises theorem. Lastly, we provide an empirical illustration using U.S. Treasury yields under a variety of priors and a comparison with other models such as the Vasicek and the 3/2 models.
