In this article we characterize and estimate the process for short-term interest rates using federal funds interest rate data. We presume that we are observing a discrete-time sample of a stationary scalar diffusion. We concentrate on a class of models in which the local volatility elasticity is constant and the drift has a flexible specification. To accommodate missing observations and to break the link between "economic time" and calendar time, we model the sampling scheme as an increasing process that is not directly observed. We propose and implement two new methods for estimation. We find evidence for a volatility elasticity between one and one-half and two. When interest rates are high, local mean reversion is small and the mechanism for inducing stationarity is the increased volatility of the diffusion process.