Bayesian forecasts for cointegrated models

This paper investigates Bayesian forecasts for some cointegrated time series data. Suppose data are derived from some cointegrated model, but, an unrestricted vector autoregressive model, without including cointegrated conditions, is fitted; the implication of using an incorrect model will be investigated from the Bayesian forecasting viewpoint. For some special cointegrated data and under the diffuse prior assumption, it can be analytically proven that the posterior predictive distributions for both the true model and the fitted model are asymptotically the same for any future step. For a more general cointegrated model, examinations are performed via simulations. Some simulated results reveal that a reasonably unrestricted model will still provide a rather accurate forecast as long as the sample size is large enough or the forecasting period is not too far in the future. For a small sample size or for long-term forecasting, more accurate forecasts are expected if the correct cointegrated model is acutally applied.