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Any decision making process that relies on a probabilistic forecast of futureevents necessarily requires a calibrated forecast. This paper proposes newmethods for empirically assessing forecast calibration in a multivariatesetting where the probabilistic forecast is given by an ensemble of equallyprobable forecast scenarios. Multivariate properties are mapped to a singledimension through a pre-rank function and the calibration is subsequentlyassessed visually through a histogram of the ranks of the observation'spre-ranks. Average ranking assigns a pre-rank based on the average univariaterank while band depth ranking employs the concept of functional band depthwhere the centrality of the observation within the forecast ensemble isassessed. Several simulation examples and a case study of temperature forecasttrajectories at Berlin Tegel Airport in Germany demonstrate that bothmultivariate ranking methods can successfully detect various sources ofmiscalibration and scale efficiently to high dimensional settings.

Assessing the calibration of high-dimensional ensemble forecasts using rank histograms