In this article we compared the forecasting accuracy of unrestricted and penalized regressions using many predictors for the Brazilian industrial production index. We focused on the least absolute shrinkage and selection operator (Lasso) and its extensions. We also proposed a combination between penalized regressions and a variable search algorithm (PVSA). Factor-based models were used as our benchmark specification. Our study produced three main findings. First, Lasso-based models over-performed the benchmark in short-term forecasts. Second, the PSVA over-performed the proposed benchmark, regardless of the horizon. Finally, the best predictive variables are consistently chosen by all methods considered. As expected, these variables are closely related to Brazilian industrial activity. Examples include vehicle production and cardboard production.