Forecast Selection for Combination with Integer Programming: a Robustness Check with a Focus on the Use of Different Estimation Windows

In this paper, we investigate the robustness of a forecast selection algorithm in which integer programming is used to select forecasts for averaging, given an estimated covariance matrix, instead of averaging over every available forecast. While numerous empirical studies on forecast combination methods fail to consistently outperform simple averaging, we are interested in whether this particular method succeeds in doing so. Using forecasts of real GDP growth and unemployment from the European Central Bank Survey of Professional Forecasters, we apply the algorithm in combination with different estimation windows. Besides considering a single expanding and a single rolling window, we use pseudo-out-of-sample cross-validation to determine optimal window size. We also combine different estimation windows using both equal weights and weights based on the pseudo-out-of-sample performance. The findings of our paper reveal that the algorithm is not robust to the estimation window used in the presence of data instability, and that improvements in forecast accuracy can be made by taking a careful look at pseudo-out-of-sample performance. Furthermore, the overall performance of the algorithm is not consistent across different panels and different horizons, as a consequence of bias in the estimation of the covariance matrix. When there is no significant indication of estimation error, the algorithm shows promising results relative to simple averaging.