On the specification of cointegrated autoregressive moving-average forecasting systems

This paper discusses equilibrium correction, echelon canonical form vector autoregressive moving-average, EC-ARMA(E), forecasting systems. The echelon canonical form of a vector ARMA model is expanded by the inclusion of an equilibrium correction term to accommodate the possibility of cointegrated variables. A coherent procedure is presented for consistently estimating the Kronecker indices, which characterize the echelon form, and the cointegration rank, which is essential in the specification of the equilibrium correction term. A method of estimation that is fully efficient under Gaussian assumptions is also discussed. The computational burden of these techniques is very moderate because they are based on least squares calculations. The methodology is illustrated by examining a six-equation model of the US economy. An improvement in forecasting performance of the selected EC-ARMA(E), model over non-equilibrium correction and previously preferred vector AR equilibrium correction models is observed. (C) 2002 International Institute of Forecasters. Published by Elsevier B.V. All rights reserved.