A plethora of static and dynamic models exist to forecast Value-at-Risk and other quantile-related metrics used in financial risk management. Industry practice tends to favour simpler, static models such as historical simulation or its variants whereas most academic research centres on dynamic models in the GARCH family. While numerous studies examine the accuracy of multivariate models for forecasting risk metrics, there is little research on accurately predicting the entire multivariate distribution. Yet this is an essential element of asset pricing or portfolio optimization problems having non-analytic solutions. We approach this highly complex problem using a variety of proper multivariate scoring rules to evaluate over 100,000 forecasts of eight-dimensional multivariate distributions: of exchange rates, interest rates and commodity futures. This way we test the performance of static models, viz. empirical distribution functions and a new factor-quantile model, with commonly used dynamic models in the asymmetric multivariate GARCH class.
Of Quantiles and Expectiles: Consistent Scoring Functions, Choquet Representations, and Forecast Rankings
In the practice of point prediction, it is desirable that forecasters receive a directive in the form of a statistical functional, such as the mean or a quantile of the predictive distribution. When evaluating and comparing competing forecasts, it is then critical that the scoring function used for these purposes be consistent for the functional at hand, in the sense that the expected score is minimized when following the directive. We show that any scoring function that is consistent for a quantile or an expectile functional, respectively, can be represented as a mixture of extremal scoring f…
Typically, point forecasting methods are compared and assessed by means of an error measure or scoring function, such as the absolute error or the squared error. The individual scores are then averaged over forecast cases, to result in a summary measure of the predictive performance, such as the mean absolute error or the (root) mean squared error. I demonstrate that this common practice can lead to grossly misguided inferences, unless the scoring function and the forecasting task are carefully matched. Effective point forecasting requires that the scoring function be specified ex ante, or tha…
Uncertainty Quantification in Forecast Comparisons
University of Wuppertal（伍珀塔尔大学）；Heidelberg Institute for Theoretical Studies（海德堡理论研究所）；Goethe University Frankfurt, Faculty of Economics and Business（法兰克福歌德大学经济与商业学院）；Marburg University, Department of Mathematics and Computer Science（马尔堡大学数学与计算机系）
