Random Forests Feature Selection on Time Series Data
Some EDA might be needed to create new features for each time-series item. You might want to mine for patterns and have random forest reduce the overfitting. Exactly how mining is done depends on the nature of the problem, which might indicate for things like: 


interesting time periods, 
events that happen at a time, 
time lag between different series,
dynamical systems,
latent variables,
scedasticity


Breiman's landmark paper on random forest gives some theoretical guarantees that random forest works well when individual classifiers are good and the correlation between these individuals are low. This can also be a heuristic to prune features.