An Oracle Inequality for Multivariate Dynamic Quantile Forecasting

Abstract

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