(in Applications and Case Studies)

Reprojecting Partially Observed Systems with Application to Interest Rate Diffusions

A. Ronald Gallant, George Tauchen
Journal of the American Statistical Association, Vol. 93, No. 441. (Mar., 1998), pp. 10-24.


We introduce reprojection as a general purpose technique for characterizing 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 observables. Secondly, system parameters are estimated by minimum chi-squared where the chi-squared criterion is a quadratic form in the expected score of the projection. Thirdly, the constraints on dynamics implied by the nonlinear system are imposed by projecting a long simulation of the estimated system onto a Hermite series representation of the constrained transition density for observables. The constrained transition density can be used to study the response of the system to its observable history. We utilize the technique to assess the dynamics of several diffusion models for the short-term interest rate that have been proposed and to compare them to a new model that has feedback from the interest rate into both the drift and diffusion coefficients of a volatility equation.

Keywords: Efficient method of moments, Nonlinear dynamic models, Partially observed state, Stochastic differential equations.