Gaussian estimation of mixed-order continuous-time dynamic models with unobservable stochastic trends from mixed stock and flow data

This paper develops an algorithm for the exact Gaussian estimation of a mixed-order continuous-time dynamic model, with unobservable stochastic trends, from a sample of mixed stock and flow data. Its application yields exact maximum likelihood estimates when the innovations are Brownian motion and either the model is closed or the exogenous variables are polynomials in time of degree not exceeding two, and it can be expected to yield very good estimates under much more general circumstances. The paper includes detailed formulae for the implementation of the algorithm, when the model comprises a mixture of first-and second-order differential equations and both the endogenous and exogenous variables are a mixture of stocks and flows.