Reprojecting Partially Observed Systems with Application to Interest Rate Diffusions

We introduce reprojection as a general purpose technique for characterizing the observable dynamics of a partially observed nonlinear system. System parameters are estimated by method of moments wherein moments implied by the system are matched to moments implied by the transition density for observables that is determined by projecting the data onto its Hermite representation. Reprojection imposes the constraints implied by the system on the transition density and is accomplished by projecting a long simulation of the estimated system onto the Hermite representation. We utilize the technique to assess the dynamics of several diffusion models for the short-term interest rate that have been proposed and compare them to a new model that has feedback from the interest rate into both the drift and diffusion coefficients of a volatility equation. This effort entails the development of new graphical diagnostics.