Finding effective weights to combine forecasts

We investigate the effectiveness of different weighting schemes to combine a set of forecasts from linear regression models. We use a set of 218=162.144 one-step ahead forecasts from a previous paper by Holtrop et al.(2014), as well as a selection of the best models, to all of which we assign a weight and create a single forecast. Our goal is to determine the effectiveness of different weighting schemes in comparison to the simple average of all the forecasts. We will evaluate the following schemes: The median, inverse MSPE weights, Bayesian Averaging, Principal Component Analysis and K-mean-clustering. The forecasts from all models will be evaluated statistically as well as economically, by creating a fictive investment strategy based on the produced forecasts. Both give somewhat different results, but the main findings are that the mean is a very solid benchmark and that other weights are most effective when using the full sample of forecasts. The inverse MSPE based weights perform the best of all the created weighting schemes for the full sample, and the K-Mean-clustering algorithm also gives promising results, especially because only a basic version of the algorithm was used. This can be an interesting weighting scheme for future research.