CRPS-based online learning for nonlinear probabilistic forecast combination

Forecast combination improves upon the component forecasts. Most often, combination approaches are restricted to the linear setting only. However, theory shows that if the component forecasts are neutrally dispersed—a requirement for probabilistic calibration—linear forecast combination will only increase dispersion and thus lead to miscalibration. Furthermore, the accuracy of the component forecasts may vary over time and the combination weights should vary accordingly, necessitating updates as time progresses. In this paper, we develop an online version of the beta-transformed linear pool, which theoretically can transform the probabilistic forecasts such that they are neutrally dispersed. We show that, in the case of stationary synthetic time series, the performance of the developed method converges to that of the optimal combination in hindsight. Moreover, in the case of nonstationary real-world time series from a wind farm in mid-west France, the developed model outperforms the optimal combination in hindsight.