Deep learning for spatio‐temporal modeling: Dynamic traffic flows and high frequency trading

Deep learning applies hierarchical layers of hidden variables to construct nonlinear high dimensional predictors. Our goal is to develop and train deep learning architectures for spatio‐temporal modeling. Training a deep architecture is achieved by stochastic gradient descent and dropout for parameter regularization with a goal of minimizing out‐of‐sample predictive mean squared error. To illustrate our methodology, we first predict the sharp discontinuities in traffic flow data, and secondly, we develop a classification rule to predict short‐term futures market prices using order book depth. Finally, we conclude with directions for future research.