Optimal forecast under structural breaks

This paper develops an optimal combined estimator to forecast out‐of‐sample under structural breaks. When it comes to forecasting, using only the postbreak observations after the most recent break point may not be optimal. In this paper, we propose a new estimation method that exploits the prebreak information. In particular, we show how to combine the estimator using the full‐sample (i.e., both the prebreak and postbreak data) and the estimator using only the postbreak sample. The full‐sample estimator is inconsistent when there is a break while it is efficient. The postbreak estimator is consistent but inefficient. Hence, depending on the severity of the breaks, the full‐sample estimator and the postbreak estimator can be combined to balance the consistency and efficiency. We derive the Stein‐like combined estimator of the full‐sample and the postbreak estimators, to balance the bias‐variance trade‐off. The combination weight depends on the break severity, which we measure by the Wu–Hausman statistic. We examine the properties of the proposed method, analytically in theory, numerically in simulation, and also empirically in forecasting real output growth across nine industrial economies.