Static and dynamic models for multivariate distribution forecasts: Proper scoring rule tests of factor-quantile versus multivariate GARCH models

• Published in: International journal of forecasting Vol. 39; no. 3; pp. 1078 - 1096
• Main Authors: Alexander, Carol, Han, Yang, Meng, Xiaochun
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.07.2023
• Subjects: Bagging; Continuous ranked probability score; Energy score; Factor quantile regression; Forecast; Historical simulation; Multivariate density; Variogram score; Continuous ranked probability score; Historical simulation; Forecast; Energy score; Multivariate density; Factor quantile regression; Variogram score; Bagging
• ISSN: 0169-2070
• DOI: 10.1016/j.ijforecast.2022.04.004

Many static and dynamic models exist to forecast Value-at-Risk and other quantile-related metrics used in financial risk management. Industry practice favours simpler, static models such as historical simulation or its variants. Most academic research focuses 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. However, this is an essential element of asset pricing or portfolio optimization problems having non-analytic solutions. We approach this highly complex problem using various proper multivariate scoring rules to evaluate forecasts of eight-dimensional multivariate distributions: exchange rates, interest rates and commodity futures. This way, we test the performance of static models, namely, empirical distribution functions and a new factor-quantile model with commonly used dynamic models in the asymmetric multivariate GARCH class.