Forecasting and Interpolation Using Vector Autoregressions with Common Trends

A modification of the vector autoregressive model is to include a stochastic trend component in each equation. It is argued that this formulation will lead to a more parsimonious model than traditional vector autoregressions formulated in terms of levels or differences. Common trends, or factors, may be introduced into the model. This leads to certain of the variables being co-integrated and, as shown in Granger and Engle [1987], the model then has an error correction representation. Estimation of the model can be carried out by casting it in state space form and applying the Kalman filter. This enables estimation to be carried out for a very general situation in which observations may be missing, temporally aggregated or observed at different time intervals. The common trends may also be extracted using smoothing techniques. Missing observations can also be estimated and the model is likely to be useful if this is the main objective.