An Oracle Inequality for Multivariate Dynamic Quantile Forecasting
39 Pages Posted: 2 May 2022 Last revised: 28 Sep 2022
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
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