Path Signatures as Universal Feature Extractors for Limit Order Book Mid-Price Prediction

We apply the path signature transform — a canonical lossless encoding of multidimensional time series rooted in Chen's theorem (1954) and Rough Path Theory (Lyons 1998) — to the joint trajectory of bid price, ask price, bid volume, and ask volume extracted from limit order book (LOB) data. Truncating the signature at order 4 yields a 341-dimensional feature vector that constitutes a sufficient statistic for predicting the next mid-price direction without any manual feature engineering. Evaluated on the FI-2010 benchmark dataset (NASDAQ, 10 stocks, 10 trading days, 10-level LOB) and on proprietary US equity tick data (2020–2024), the signature feature set outperforms standard hand-crafted LOB features (OBI, spread, VPIN, microprice) by 35–56% in terms of Information Coefficient (IC) at 100–500ms prediction horizons. The 5 most informative signature terms have direct microstructure interpretations rooted in Kyle (1985) and Glosten-Milgrom (1985) frameworks. GPU-accelerated computation via the Signatory library achieves full 341-feature extraction in under 0.8ms, making the approach compatible with live HFT deployment.