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Title: Using L2 and kernel scores to optimise combinations of density forecasts Authors:  Xiaochun Meng - University of Sussex (United Kingdom) [presenting]
James Taylor - University of Oxford (United Kingdom)
Abstract: Combining density forecasts has become common practice for various applications. The optimal weights are often obtained by minimising a chosen proper scoring rule, where the log score is most commonly used in the literature. Unfortunately, with the log score, closed-form solutions generally do not exist for the combining weights. We optimise the weights by minimising L2 and kernel scores. We establish the closed-form representations for the optimal weights, and then use them to incorporate a time-varying structure to provide further improvement in forecast accuracy. We use simulated and real data to illustrate our results.