Combining and Evaluating Probabilistic Forecasts (original) (raw)

Combination of forecasts: A bibliography

Research Papers in Economics, 1998

During the past thirty years, there has been considerable concern about combination of forecasts. Many of the articles and books dedicated to this specific area explain and demonstrate that combining multiple individual forecasts can improve forecast accuracy. The improvement in accuracy mainly depends on forecast combination techniques which range from simple combinations like averaging the forecasts to more complex ones that use the Bayesian approach. This paper provides a bibliography of selected articles and books related to the combination of forecasts in various disciplines and is intended to be a catalog for locating contributions in research areas focusing on the theory and applications of combining forecasts. The bibliography includes recent articles and is as up-to-date as possible.

Combining Forecasting Procedures: Some Theoretical Results

2000

We study some methods of combining procedures for forecasting a continuous random variable. Statistical risk bounds under the square error loss are obtained under mild distributional assumptions on the future given the current outside information and the past observations. The risk bounds show that the combined forecast automatically achieves the best performance among the candidate procedures up to a constant factor and an additive penalty term. In term of the rate of convergence, the combined forecast performs as well as if one knew which candidate forecasting procedure is the best in advance.

Probabilisitic forecasts in hierarchical time series

2018

Forecast reconciliation involves adjusting forecasts to ensure coherence with aggregation constraints. We extend this concept from point forecasts to probabilistic forecasts by redefining forecast reconciliation in terms of linear functions in general, and projections more specifically. New theorems establish that the true predictive distribution can be recovered in the elliptical case by linear reconciliation, and general conditions are derived for when this is a projection. A geometric interpretation is also used to prove two new theoretical results for point forecasting; that reconciliation via projection both preserves unbiasedness and dominates unreconciled forecasts in a mean squared error sense. Strategies for forecast evaluation based on scoring rules are discussed, and it is shown that the popular log score is an improper scoring rule with respect to the class of unreconciled forecasts when the true predictive distribution coheres with aggregation constraints. Finally, evid...

A non-linear combination of experts' forecasts: A Bayesian approach

Journal of Forecasting, 1994

A general Bayesian approach to combining n expert forecasts is developed. Under some moderate assumptions on the distributions of the expert errors, it leads to a consistent, monotonic, quasi-linear average formula. This generalizes Bordley's results.

To combine or not to combine? issues of combining forecasts

Journal of Forecasting, 1992

ABSTRACT This paper addresses issues such as: Does it always pay to combine individual forecasts of a variable? Should one combine an unbiased forecast with one that is heavily biased? Should one use optimal weights as suggested by Bates and Granger over twenty ...

Combining probability forecasts

Journal of the Royal Statistical Society: Series B (Statistical Methodology), 2010

Linear pooling is by the far the most popular method for combining probability forecasts. However, any nontrivial weighted average of two or more distinct, calibrated probability forecasts is necessarily uncalibrated and lacks sharpness. In view of this, linear pooling requires recalibration, even in the ideal case in which the individual forecasts are calibrated. Toward this end, we propose a beta transformed linear opinion pool (BLP) for the aggregation of probability forecasts from distinct, calibrated or uncalibrated sources. The BLP method fits an optimal nonlinearly recalibrated forecast combination, by compositing a beta transform and the traditional linear opinion pool. The technique is illustrated in a simulation example and in a case study on statistical and National Weather Service probability of precipitation forecasts.