@phdthesis{Schulz2023, author = {Schulz, Felix}, title = {Integrated models for the selection and weighting of individual opinions and forecasts in expectation and forecast combination}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:824-opus4-8478}, school = {Katholische Universit{\"a}t Eichst{\"a}tt-Ingolstadt}, year = {2023}, abstract = {In forecast combination, multiple predictions are linearly combined through the assignment of weights to individual forecast models or forecasters. Various approaches exist for defining the weights, which typically involve determining the number of models to be used for combination (selection), choosing an appropriate weighting function for the forecast scenario (weighting), and using regularization techniques to adjust the calculated weights (shrinkage). The papers listed address the integration of the three approaches into holistic data analytical models. The first paper develops a two-stage model in which weights are first calculated based on the in-sample error covariances to minimize the error on the available data by combining the individual models. Based on the selection status of a model, the weight of an individual model is then linearly shrunk either toward the mean or toward zero. The selection status is thereby derived apriori from information criteria, where Contribution 1 introduces the selection based on the model's in-sample accuracy and performance robustness under uncertainty. Contribution 2 modifies the two-stage model to shrink the forecasters' weights non-proportionally to the mean or zero. Further, a new information criterion based on forward feature selection is proposed that iteratively selects the forecaster that is expected to achieve the largest increase in accuracy when combined. Contribution 3 extends the iteration-based information criterion presented in the second contribution to consider diversity gains in addition to accuracy gains when selecting and combining forecasters. A one-stage model for simultaneous weighting, shrinking, and selection is finally built and evaluated on simulated data in Contribution 4. Instead of requiring a prior selection criterion, the model itself learns which forecasters to shrink to the mean or to zero, while relying on a new sampling procedure to tune the model.}, subject = {Prognoseverfahren}, language = {en} }