Discrete time representation of stationary and non-stationary continuous time systems

This paper derives the formulae for an exact discrete time representation corresponding to a system of higher-order stochastic differential equations. The formulae are applicable in stationary, non-stationary and explosive systems and for data observed as a mixture of both stock and flow variables. Expressions are also provided for an explicit moving average representation of the disturbance vector in the discrete time model, which can be used, under the assumption of white noise continuous time disturbances, to derive formulae for the computation of the exact Gaussian likelihood function.