This paper introduces composite absolute value and sign (CAVS) forecasts, a nonlinear framework that combines forecasts of the sign and absolute value of a time series into conditional mean forecasts. In contrast to linear models, the proposed framework allows different predictors to impact the sign and absolute value of the target series. Among other results, I show that the conditional mean can be written as a function of mean squared error optimal sign and absolute value forecasts. An empirical application using the FRED-MD dataset shows that CAVS forecasts substantially outperform linear forecasts for series that exhibit persistent volatility dynamics, such as output and interest rates. The empirical application highlights that exploiting nonlinearities in macroeconomic series improves forecast accuracy.

We conduct an out-of-sample backtesting exercise of Growth-at-Risk (GaR) predictions for 24 OECD countries. We consider forecasts constructed from quantile regression and GARCH models. The quantile regression forecasts are based on a set of recently proposed measures of downside risks to GDP, including the national financial condition index. The backtesting results show that quantile regression and GARCH forecasts have a similar performance. If anything, our evidence suggests that standard volatility models such as the GARCH(1,1) are more accurate.

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 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 substantially reduce extreme dependence across VaR violations.