Static and Dynamic Models for Multivariate Distribution Forecasts: Proper Scoring Rule Tests of Factor-Quantile vs. Multivariate GARCH Models

Abstract: 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.