Forecasting of seasonal cointegrated processes

In this paper, forecasts of seasonally cointegrated models are analysed applying the maximum likelihood approach for seasonal cointegration suggested by Lee. The forecasts of seasonally cointegrated models in fourth differences are compared with those in first differences, including seasonal dummies. The comparison is done by means of simulating various bivariate data generating processes containing seasonal cointegrating relationships. Forecasts are calculated for different specifications of lag length and cointegrating rank. One main result of the simulation study is that the models in first differences with seasonal dummies forecast smaller errors for short horizons than the seasonally cointegrated models. For longer forecast horizons models in fourth differences outperform the former. Furthermore, a model with more seasonal cointegrating relations than in the underlying model produces very high forecast errors. This is not affected by the choice of the lag length. Both modelling procedure are applied to the German income–consumption–wealth process. The forecast results of the models confirm the evidence of the simulation study.