Ask CARL: Forecasting tail probabilities for energy commodities

We use a set of conditional auto-regressive logit (CARL) models to predict tail probabilities for returns calculated from futures of four energy commodities. We show that CARL models are very useful to forecast the probability of tail events in energy markets and the forecasting ability of the models generally increases when commodity implied volatility is added as a predictor. We further present new bivariate models to jointly forecast the probabilities that returns from a given commodity and from the S&P 500 index are on the left tail and models for the coexceedances. We find that CARL family models have always a better forecasting performance than GARCH and Quantile-Augmented Volatility models in a univariate and multivariate setting. Conversely, when modelling coexceedances, CARL models exhibit a better predictive capacity only for Brent and heating oil.