Formulating and estimating continuous time rational expectations models

"This paper proposes a method for estimating the parameters of continuous time, stochastic rational expectations models from discrete time observations. The method is important since various heuristic procedures for deducing the implications for discrete time data of continuous time models, such as replacing derivatives with first differences, can sometimes give rise to very misleading conclusions about parameters. Our proposal is to express the restrictions imposed by the rational expectations model on the continuous time process generating the observable variables. Then the likelihood function of a discrete time sample of observations from this process is obtained. Parameter estimates are computed by maximizing the likelihood function with respect to the free parameters of the continuous time model"--Federal Reserve Bank of Minneapolis web site.