Multivariate probabilistic forecasting using Bayesian model averaging and copulas

TL;DR

This paper introduces a novel approach combining Bayesian model averaging and Gaussian copulas to produce well-calibrated multivariate weather forecasts, effectively capturing dependencies between variables.

Contribution

It presents a new method that integrates univariate BMA post-processing with copulas to recover joint dependence in multivariate weather forecasting.

Findings

Improves calibration and sharpness of forecasts.

Recovers known dependencies between weather variables.

Outperforms raw ensemble and non-joint methods.

Abstract

We propose a method for post-processing an ensemble of multivariate forecasts in order to obtain a joint predictive distribution of weather. Our method utilizes existing univariate post-processing techniques, in this case ensemble Bayesian model averaging (BMA), to obtain estimated marginal distributions. However, implementing these methods individually offers no information regarding the joint distribution. To correct this, we propose the use of a Gaussian copula, which offers a simple procedure for recovering the dependence that is lost in the estimation of the ensemble BMA marginals. Our method is applied to 48-h forecasts of a set of five weather quantities using the 8-member University of Washington mesoscale ensemble. We show that our method recovers many well-understood dependencies between weather quantities and subsequently improves calibration and sharpness over both the raw ensemble and a method which does not incorporate joint distributional information.