This article derives the exact discrete representation corresponding to a cointegrated system of mixed first‐ and second‐order stochastic differential equations with mixed stock and flow data and observable stochastic trends. We provide some formulae to implement the Gaussian estimation and conduct a Monte Carlo experiment to examine the finite sample properties of the Gaussian estimator. We also compare the properties of the estimator based on the exact discrete representation to that based on misspecified discrete models. Results show that the use of the exact discrete representation for estimation purposes produces considerable reductions in the root mean square error of the estimate for most of the parameters.