In this paper the econometric analysis of linear quadratic adjustment cost models with rational expectations and cointegrated variables is extended to a multi-equational set-up and the case of second-order adjustment costs. The proposed method is based on the idea of nesting the system of interrelated Euler equations stemming from the intertemporal optimization problem within a cointegrated Vector Equilibrium Correction Model representing the agent forecast tool. Contrary to previous practise a likelihood-based procedure can be set out without appealing to numerical optimization algorithms. Cointegration and generalized least squares techniques can be used to estimate and test the model.