Particle Filtering and Inference for Limit Order Books in High Frequency Finance

This paper investigates the on-line analysis of high-frequency financial order book data using Bayesian modelling techniques. Order book data involves evolving queues of orders at different prices, and here we propose that the order book shape is proportional to a gamma or inverse-gamma density function. Inference for these models is implemented on-line using particle filters and evaluated on a high-frequency EURUSD foreign exchange limit order book. The two possible order book shapes are tested using particle filter marginal likelihood estimates and in addition, heat maps are constructed based on the inference results to reveal the imbalance of order distributions between the two sides of an order book, thereby offering valuable insights into the movements of future prices.