An Oracle Inequality for Multivariate Dynamic Quantile Forecasting

40 Pages Posted: 2 May 2022 Last revised: 6 Jul 2022

See all articles by Jordi Llorens-Terrazas

Jordi Llorens-Terrazas

Universitat Pompeu Fabra; Barcelona School of Economics

Date Written: April 25, 2022


This paper derives an oracle inequality for a class of misspecified multivariate conditional autoregressive quantile forecasts. The class is a special case of the ''VAR for VaR'' of White, Kim and Manganelli (2015). This inequality is used to establish that the predictor that minimizes the in-sample average check loss achieves the best out-of-sample performance within its class at a near optimal rate, even when the model is fully misspecified. An empirical application to backtesting global Growth-at-Risk shows that a combination of the AR-GARCH and VAR for VaR methodologies performs best out-of-sample in terms of the check loss.

Keywords: Multivariate conditional quantile, oracle inequality, time series, forecasting, Markov chain.

JEL Classification: C14, C22, C53, C58

Suggested Citation

Llorens-Terrazas, Jordi, An Oracle Inequality for Multivariate Dynamic Quantile Forecasting (April 25, 2022). Available at SSRN: or

Jordi Llorens-Terrazas (Contact Author)

Universitat Pompeu Fabra ( email )


Barcelona School of Economics ( email )

Carrer de Ramon Trias Fargas, 25-27
Barcelona, 08005

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