  We have applied a Long Short-Term Memory neural network to model S&P 500
volatility, incorporating Google domestic trends as indicators of the public
mood and macroeconomic factors. In a held-out test set, our Long Short-Term
Memory model gives a mean absolute percentage error of 24.2%, outperforming
linear Ridge/Lasso and autoregressive GARCH benchmarks by at least 31%. This
evaluation is based on an optimal observation and normalization scheme which
maximizes the mutual information between domestic trends and daily volatility
in the training set. Our preliminary investigation shows strong promise for
better predicting stock behavior via deep learning and neural network models.
