Recurrent Neural Networks with more flexible memory: better predictions
  than rough volatility
Damien Challet Vincent Ragel
We extend recurrent neural networks to include several flexible timescales
for each dimension of their output, which mechanically improves their abilities
to account for processes with long memory or with highly disparate time scales.
We compare the ability of vanilla and extended long short term memory networks
(LSTMs) to predict asset price volatility, known to have a long memory.
Generally, the number of epochs needed to train extended LSTMs is divided by
two, while the variation of validation and test losses among models with the
same hyperparameters is much smaller. We also show that the model with the
smallest validation loss systemically outperforms rough volatility predictions
by about 20% when trained and tested on a dataset with multiple time series.