Predicting Exchange Rate Volatility in Brazil: an approach using quantile autoregression

We apply quantile regression in some of its new formulations to analyze exchange rate volatility. We use the conditional autoregressive value at risk (CAViaR) model of Engle and Manganelli (2004), which applies autoregressive functions to quantile regression to estimate volatility. That model has proved effective when compared to others for various purposes. We not only compare the forecasting power of models based on quantile regression with some models of the GARCH family, but also examine the behavior of the exchange rate along its conditional distribution and its consequent volatility. When applying CAViaR in the whole distribution, our results show differentiation of the angular coefficients for each quantile interval of the distribution for the asymmetric CAViaR model. With respect to the exchange rate volatility, we build forecasts from 60 models and use two models as reference to apply the predictive ability test of Giacomini and White (2006). The results indicate that the prediction of the asymmetric CAViaR model with quantile interval of (1, 99) is better than (or equal to) 66% of the models and worse than 34%. In turn, the other benchmark model, the GARCH (1,1), is worse than 71% of the models, better than 13%, and equal in forecasting precision to 16% of the models.