9730305 Ait-Sahalia Interest rates have traditionally been modeled in the economics literature as following continuous-time Markov processes, and more specifically diffusions. By contract, recent term structure models often imply non-Markovian continuous-time dynamics. Can discretely sampled interest rate data help decide which continuous-time models are sensible? Within the Markovian world, diffusion processes are characterized by the continuity of their sample paths. It is immediately obvious that this condition cannot be verified from the observed sample path. By nature, even if the sample path were continuous, the discretely sampled interest rate data will appear as a sequence of discrete changes. This is a fundamental and very important problem in financial economics. This project examines whether the discontinuities observed in the discrete data are the result of discreteness of sampling, or rather evidence of genuine non-diffusion dynamics of the continuous-time interest rate process. The issue is to isolate the observable implications for the data of being an incomplete discrete sample from a continuous-time diffusion. The project relies on testing a necessary and sufficient restriction on the condition densities of diffusions, at the sampling interval of the observed data. This restriction characterizes the continuity of the unobservable complete sample path. This project investigates the distribution, consistency and power properties of the test statistics. The tests will be implemented empirically. ??
