On Forecasting Cointegrated Seasonal Time Series

We analyze periodic and seasonal cointegration models for bivariate quarterly observed time series in an empirical forecasting study. We include both single equation and multiple equation methods. A VAR model in first differences with and without cointegration restrictions is also included in the analysis, where it serves as a benchmark. Our empirical results indicate that the VAR model in first differences without cointegration is best if one-step and four-step ahead forecasts are considered. For longer forecast horizons, however, the periodic and seasonal cointegration models are better. When comparing periodic versus seasonal cointegration models, we find that the seasonal cointegration models tend to yield better forecasts. Finally, there is no clear indication that multiple equation methods improve on single equation methods.