We conduct an out-of-sample backtesting exercise of multivariate Growth-at-Risk (GaR) predictions for 24 OECD countries. We consider forecasting methods based on quantile regression (QR) and GARCH models. We find evidence of predictability up to one year ahead, and the forecasts based on GARCH models dominate those based on QR. Our empirical evidence supports the view that the time-varying dynamics of the lower quantiles of GDP growth cannot be distinguished from those implied by time-varying volatility.

We introduce a framework to evaluate collections of interval forecasts for multiple time series. We propose an evaluation criteria based on the dependence properties of the forecasts. Our criteria assumes that a forecaster prefers, ceteris paribus, the collection that minimizes the probability of simultaneous interval forecast violations for a large number of time series. The evaluation of the collections is carried out by means of a simple loss function and we establish that, under mild assumptions, such a loss leads to consistent ranking of the forecasts. We apply our framework to evaluate commonly used Value-at-Risk (VaR) forecasting methods for all S&P 500 stocks. We find that methods that take the factor structure of volatility into account reduce the dependence across VaR violations.