Non-parametric prediction in a limit order book

Many securities markets are organized as double auctions where each incoming limit order-i.e., an order to buy or sell at a specific price-is stored in a data structure called the limit order book [1]. A trade happens whenever a marketable order arrives-i.e., an order to buy or sell at the best currently available price on the opposite side of the order book. This order flow is visible to every market participant in real time. The mid-price is defined as the average of the best offer and best bid prices. We propose a novel non-parametric approach to short-term forecasting of the mid-price change in a limit order book. We construct a state characterizing the order book at each time instant, cluster the states, and compute a feature vector for each cluster. The features get updated during the course of a trading day, as new orders arrive. Our prediction rules at every time instant during the trading day are based on the feature vector of the cluster observed at that time instant. We test our predictor by applying it to an order execution problem.