A0425
Title: Evaluation of copula forecasts
Authors: Tobias Fissler - Vienna University of Economics and Business (Austria) [presenting]
Abstract: Forecasts for uncertain events $Y$ provide guidance in decision-making. The past decades have witnessed a paradigm shift from point forecasts to distributional forecasts, capturing the inherent uncertainty of $Y$. The accuracy of distributional forecasts is evaluated in terms of scoring rules, which assign to each predictive distribution $F$ and observation from $Y$ a penalty $S(F,Y)$. To incentivise truthful forecasts, scoring rules should be (strictly) proper, meaning that the expected score is (strictly) minimised by the correctly specified distribution of $Y$. If $Y$ is multivariate, the predictive distribution can be decomposed into the marginals and the copula, capturing the dependence structure. It has been an open problem if there exist strictly proper copula scores $S_{Copula}$ in the sense that the arguments are a predictive copula $C$ and an observation $Y$, and the expectation over $Y$ is strictly minimised by providing the correct copula of $Y$. It will be shown that such strictly proper copula scores cannot exist. As a remedy, the usage of bivariate scores equipped with the lexicographic order is suggested and discussed. They decouple the influence of predictive marginal distributions and the predictive copula. As such, they are a tool to control if a predictive distribution outperforms another one based on its marginals or its copula.
