Finite sample forecast properties and window length under breaks in cointegrated systems

We show that extending the estimation window prior to structural breaks in cointegrated systems can be beneficial for forecasting performance and highlight under which conditions. In doing so, we generalize the Pesaran & Timmermann (2005)'s forecast error decomposition and show 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. We also derive new expressions for the estimators of the adjustment matrix and a constant, which are auxiliary to the decomposition. Finally, we introduce new simulation based estimators for the finite sample forecast properties which are based on the derived decomposition. Our finding points out that, in some cases, we can neglect parameter instability by extending the window backward and be insured against higher forecast risk under this model class as well, generalizing Pesaran & Timmermann (2005)'s result. Our result gives renewed importance to break tests, in order to distinguish cases when break-neglection is (not) appropriate.