Econometrica: May, 1972, Volume 40, Issue 3

Econometric Estimation of Stochastic Differential Equation Systems

https://doi.org/0012-9682(197205)40:3<565:EEOSDE>2.0.CO;2-F
p. 565-577

C. R. Wymer

An exact discrete model is derived from a recursive model consisting of a set of rth order stochastic linear differential equations with constant coefficients such that observations generated at equidistant points of time by the differential system satisfy the discrete model irrespective of the length of sampling interval. The difficulty of estimating the exact model subject to a priori restrictions makes it necessary to approximate the differential system by a non-recursive discrete model that maintains the structural form. This discrete model has a moving average disturbance term of order r - 1, but the co-variance function of this process is approximated by a function that is independent of the parameters of the continuous model. The eigenvalues and eigenvectors of the approximations to the differential system as well as their asymptotic variance matrices are also derived but, like the approximate asymptotic variance matrices of the parameter estimates, these variances are about biased probability limit