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

Abstract

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.