Feature selection for time series prediction
You don’t need to select variables for feeding to network, deep neural networks (DNN) will do this automatically. Actually DNN gives more importance to relevant variables by setting its weights. After setting the weights, some of the hidden nodes take 0 and some of them take 1 (because of sigmoid function). You can think of this 1 and 0’s as choosing relevant variables, too.

By the way, correlation matrix can not be used to select relevant variables directly. If you want to reduce the number of variables that are fed to DNN, you can use PCA. Actually PCA components are calculated by getting the Eigen-vectors of correlation matrix.