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

Carol Alexander, Yang Han, Xiaochun Meng

Research output: Contribution to journalArticlepeer-review

1 Citation (SciVal)


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.

Original languageEnglish
Pages (from-to)1078-1096
Number of pages19
JournalInternational Journal of Forecasting
Issue number3
Early online date13 Jun 2022
Publication statusPublished - 1 Jul 2023

Bibliographical note

Publisher Copyright:
© 2022 The Author(s)


  • Bagging
  • Continuous ranked probability score
  • Energy score
  • Factor quantile regression
  • Forecast
  • Historical simulation
  • Multivariate density
  • Variogram score

ASJC Scopus subject areas

  • Business and International Management

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