We investigated the predictability of the Brazilian exchange rate at High Frequency (1, 5 and 15 minutes), using local and global economic variables as predictors. In addition to the Linear Regression method, we use Machine Learning algorithms such as Ridge, Lasso, Elastic Net, Random Forest and Gradient Boosting. When considering contemporary predictors, it is possible to outperform the Random Walk at all frequencies, with local economic variables having greater predictive power than global ones. Machine Learning methods are also capable of reducing the mean squared error. When we consider only lagged predictors, it is possible to beat the Random Walk if we also consider the Brazilian Real futures as an additional predictor, for the frequency of one minute and up to two minutes ahead, confirming the importance of the Brazilian futures market in determining the spot exchange rate.