A Signature Transform of Limit Order Book Data for Stock Price Prediction

A novel approach is presented for predicting the mean-mid stock price by utilizing high-frequency and complex limit order book (LOB) data as inputs for machine learning algorithms. Specifically, the proposed approach uses rough path theory to extract signature path features from the LOB data and compresses them for training machine learning models. We compare the performance of this approach to standard autoregression methods and demonstrate its superior performance in terms of model prediction error. In addition, we use deep neural networks (DNN) and random forest (RF) to further test the proposed approach's performance compared to standard approaches using raw LOB data. The findings show that Sig-DNN, DNN with signature features, outperforms DNN with raw LOB data in terms of prediction error and efficiency, while Sig-RF, RF with signature features, underperformed RF with raw LOB data in terms of prediction but not in efficiency. We evaluate the proposed approach on multiple exchanges, including the Johannesburg and New York Stock Exchanges, and the results demonstrate better prediction error and efficiency performance in developed markets compared to emerging markets. Overall, the study highlights the potential of using signature path features with machine learning techniques for predicting the mean-mid stock price.