Optimal forecast combination under asymmetric loss and regime-switching

Forecast combinations have been repeatedly shown to outperform individual professional forecasts and complicated time series models in accuracy. Their ease of use and accuracy makes them important tools for policy decisions. While simple combinations work remarkably well in some situations, time-varying combinations can be even more accurate in other real-life scenarios involving economic forecasts. This paper uses a regime switching framework to model the time-variation in forecast combination weights. I use an optimization problem based on asymmetric loss functions in deriving optimal forecast combination weights. The switching framework is based on the work of Elliott and Timmermann (2005), however I extend their setup by using asymmetric quadratic loss in the optimization problem. This is an important extension, since with my setup it is possible to quantify and analyze optimal forecast biases for different directions and levels of asymmetry in the loss function, contributing to the vast literature on forecast bias. I interpret the equations for the optimal weights through analytical examples and examine how the weights depend on the model parameters, the level of asymmetry of the loss function and the transition probabilities and starting state.