# Deep Learning for Spatio-Temporal Modeling: Dynamic Traffic Flows and High Frequency Trading

## TL;DR

This paper develops deep learning architectures for spatio-temporal modeling, demonstrating their effectiveness in predicting traffic flow discontinuities and short-term market price movements using high-frequency trading data.

## Contribution

It introduces a methodology for training deep neural networks with SGD and dropout for spatio-temporal prediction tasks in traffic and finance.

## Key findings

- Successfully predicted sharp traffic flow discontinuities.
- Developed a classification rule for short-term market price prediction.
- Demonstrated deep learning's effectiveness in high-dimensional spatio-temporal data.

## Abstract

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 (SGD) and drop-out (DO) for parameter regularization with a goal of minimizing out-of-sample predictive mean squared error. To illustrate our methodology, we predict the sharp discontinuities in traffic flow data, and secondly, we develop a classification rule to predict short-term futures market prices as a function of the order book depth. Finally, we conclude with directions for future research.