  Recurrent neural networks (RNNs) are more suitable for learning non-linear
dependencies in dynamical systems from observed time series data. In practice
all the external variables driving such systems are not known a priori,
especially in economical forecasting. A class of RNNs called Error Correction
Neural Networks (ECNNs) was designed to compensate for missing input variables.
It does this by feeding back in the current step the error made in the previous
step. The ECNN is implemented in Python by the computation of the appropriate
gradients and it is tested on stock market predictions. As expected it out
performed the simple RNN and LSTM and other hybrid models which involve a
de-noising pre-processing step. The intuition for the latter is that de-noising
may lead to loss of information.
