(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.
Abstract
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.