An Oracle Inequality for Multivariate Dynamic Quantile Forecasting

39 Pages Posted: 2 May 2022 Last revised: 28 Sep 2022

See all articles by Jordi Llorens-Terrazas

Jordi Llorens-Terrazas

Universitat Pompeu Fabra; Barcelona School of Economics

Date Written: April 25, 2022


I derive an oracle inequality for a family of possibly misspecified multivariate conditional autoregressive quantile models. The family includes standard specifications for (nonlinear) quantile prediction proposed in the literature. 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 generalized autoregressive conditionally heteroscedastic model and the vector autoregression for Value-at-Risk 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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