Efficient Computation of Lead–Lag Signature Features for Financial Time‐Series Forecasting

We develop an efficient algorithm for computing lead–lag signature features derived from rough path theory and evaluate its application to financial return prediction. The path signature provides a universal nonlinear feature map for sequential data, but naïve computation is intractable as truncation depth grows. We exploit the algebraic structure of Chen's identity to derive incremental updates for depth‐2 signatures, achieving substantially lower computational complexity, and prove that the resulting algorithm is numerically stable. The lead–lag transformation embeds univariate series into a two‐dimensional path, recovering realized quadratic variation as the Lévy area—a quantity lost in one‐dimensional signatures. In an empirical evaluation on a panel of financial assets spanning equities, fixed income, currencies, commodities, and cryptocurrency, signature features yield their largest gains over technical indicators on long‐duration Treasuries, where bond convexity creates path‐dependent return dynamics; they offer little incremental advantage on equities, where simple momentum features perform best. We further document a divergence between statistical predictability and economic profitability: a signature‐based gold strategy attains a high backtested Sharpe ratio despite a negative unconditional correlation between forecasts and realized returns.