The effect of estimating parameters on long-term forecasts for cointegrated systems

This paper concerns Long-term forecasts for cointegrated processes. First, it considers the case where the parameters of the model are known. The paper analytically shows that neither cointegration nor integration constraint matters in Long-term forecasts. It is an alternative implication of Long-term forecasts for cointegrated processes, extending the results of previous influential studies. The appropriate Mote Carlo experiment supports our analytical result. Secondly, and more importantly, it considers the case where the parameters of the model are estimated. The paper shows that accuracy of the estimation of the drift term is crucial in Long-term forecasts. Namely, the relative accuracy of various Long-term forecasts depends upon the relative magnitude of variances of estimators of the drift term. It further experimentally shows that in finite samples the univariate ARIMA forecast, whose drift term is estimated by the simple time average of differenced data, is better than the cointegrated system forecast, whose parameters are estimated by the well-known Johansen's ML method. Based upon finite sample experiments, it recommends the univariate ARIMA forecast rather than the conventional cointegrated system forecast in finite samples for its practical usefulness and robustness against model misspecifications.