Predicting stock movements in the market its known to be an extremely difficult task. More than that, the predictability of the series itself is a controversial matter. The present study investigates if this difficulty could be alleviated by choosing specific windows of time where a more structured dynamic prevails, and whether the identification of those moments could be learned from past data. In order to do that, a novel framework is proposed. This framework is called the Predictability Crawler (P-Craw). It uses optimizations routines such as the Particle Swarm Optimization (PSO) or Genetic Algorithms (GA) to select subsets of historical data where statistical learning algorithms can be more efficiently trained. To access the accuracy of the method, it is tested against two different datasets. First, simulated data with varying percentage of noise is generated and used. In the simulations, The P-Craw is able to reliably identify the optimal subsets in scenarios ranging from 20 percent to 100 percent of predictable samples in the data. Second, intraday data from the Brazilian stocks exchange (BOVESPA) is collected and aggregated into feature and target matrices. When benchmarked against training with the whole samples in the BOVESPA data, the framework is able to significantly raise the correct directional changes of the trained models while reducing the Mean Absolute Error in up to 19 percent.