Copula Calibration of Multivariate Probabilistic Forecasts

• Activity Number: 184
• Type: Contributed
• Date/Time: Monday, August 5, 2013 : 10:30 AM to 12:20 PM
• Sponsor: IMS
• Author(s): Johanna F. Ziegel*+ and Tilmann Gneiting
• Companies: University of Bern and Heidelberg University
• Keywords: Calibration ; Forecast verification ; Probabilistic forecasts ; Probability integral transform

Abstract

We introduce new notions of calibration for multivariate probabilistic forecasts. The first one is called probabilistic copula calibration and is a natural multivariate analogue of probabilistic calibration in the univariate setting. Probabilistic copula calibration can be assessed empirically by checking for uniformity of the so-called copula probability integral transform (copula PIT) histogram. This is similar to the univariate case, where probabilistic calibration is assessed via the PIT histogram. The copula PIT histogram generalizes the multivariate rank histogram, which has been introduced as a tool for checking calibration of ensemble forecasts. However, the copula PIT histogram is not limited to ensemble forecasts. It is applicable to any multivariate forecast, including density forecasts or ensemble forecasts. The second notion of calibration that we study is climatological copula calibration. It provides an analogy to marginal calibration in the univariate setting. We illustrate our methodology in a simulation study and apply it to EMOS forecasts of bivariate wind vectors.