Enhanced approaches to the combination of forecasts

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Many important decisions rely on forecasts for future developments of key variables. Decision-makers often face multiple forecasts for these variables and typically combine them rather than selecting a single one. The standard approach focuses on one target variable at a time, employing a linear combination of forecasts. This work enhances the univariate linear combination method in two ways. First, it introduces a linear plus quadratic setup for combining univariate forecasts, offering a non-linear alternative that may yield more accurate predictions, akin to a higher-order Taylor approximation. Second, it addresses multiple target variables simultaneously, allowing for linear combination of forecasts for vector-valued variables. This method leverages interactions among components of the target vector and forecasts. The book derives optimal combination parameters for minimizing mean square prediction error for each approach and identifies suitable linear regression models to facilitate implementation. Finally, the new methods are numerically evaluated for their potential, empirical performance, and results from simulation studies.