REPROJECTING PARTIALLY OBSERVED SYSTEMS WITH APPLICATION TO INTEREST-RATE DIFFUSIONS

We introduce reprojection as a general purpose technique for character izing the dynamic response of a partially observed nonlinear system to its observable history. Reprojection is the third step of a procedure wherein first data are summarized by projection onto a Hermite series representation of the unconstrained transition density for observable s; second, system parameters are estimated by minimum chi-squared, whe re the chi-squared criterion is a quadratic form in the expected score of the projection; and third, the constraints on dynamics implied by the nonlinear system are imposed by projecting a long simulation of th e estimated system onto a Hermite series representation of the constra ined transition density for observables. The constrained transition de nsity can be used to study the response of the system to its observabl e history. We utilize the technique to assess the dynamics of several diffusion models for the short-term interest rate that have been propo sed and to compare them to a new model that has feedback from the inte rest rate into both the drift and diffusion coefficients of a volatili ty equation.