Finite Sample Forecast Properties and Window Length Under Breaks in Cointegrated Systems

The author shows that extending the estimation window prior to structural breaks in cointegrated systems can be beneficial for forecasting performance and highlights under which conditions. In doing so, the author generalizes the Pesaran and Timmermann (2005)’s forecast error decomposition and shows that it depends on four terms: (1) a period ahead risk; (2) a bias due to a conditional mean shift; (3) a bias due to a variance mismatch; (4) a gap term valid only conditionally. The author also derives new expressions for the estimators of the adjustment matrix and a constant, which are auxiliary to the decomposition. Finally, the author introduces new simulation-based estimators for the finite sample forecast properties which are based on the derived decomposition. The author’s finding points out that, in some cases, parameter instability can be neglected by extending the window backward and forecasters can be insured against higher forecast risk under this model class as well, generalizing Pesaran and Timmermann (2005)’s result. The author’s result gives renewed importance to break tests, in order to distinguish cases when break-neglection is (not) appropriate.