DeltaLag: Learning Dynamic Lead-Lag Patterns in Financial Markets

—

DeltaLag: Learning Dynamic Lead-Lag Patterns in Financial Markets

Wanyun Zhou
Saizhuo Wang
Mihai Cucuringu
Zihao Zhang
Xiang Li
Jian Guo
Chao Zhang
Xiaowen Chu
Published on 11/1/2025
Equities
Stocks
Machine learning
Deep learning
Momentum
Pairs trading
Stock picking

DeltaLag introduces the first end-to-end deep learning framework for discovering and exploiting dynamic lead-lag relationships in financial markets. Unlike traditional two-step statistical approaches that assume persistent lead-lag patterns, DeltaLag uses a sparsified cross-attention mechanism to adaptively identify, for each target stock, its top-k leading stocks and their corresponding optimal lag values on a daily basis. The model encodes historical price-volume features via a temporal encoder (e.g., LSTM), computes attention scores between the target's query and candidate leaders' key sequences over a range of lags, and selects the top-k pairs. The raw features of the identified leaders at their lagged times are then aggregated via attention weights and fed into an MLP to predict the target's next-day return. A monotonic logistic ranking loss is employed to optimize cross-sectional stock rankings directly, enhancing trading performance in long-short portfolios.

Empirical evaluations on US equities from 2010 to 2023 across S&P 500, NASDAQ, and NYSE markets demonstrate that DeltaLag significantly outperforms fixed-lag and self-lead-lag baselines, confirming the importance of dynamic, pair-specific lags and cross-asset dependencies. It also surpasses methods relying on precomputed lead-lag graphs from statistical correlations, highlighting the weak momentum of lead-lag relationships and the need for adaptive detection. Furthermore, DeltaLag achieves superior cumulative returns and Sharpe ratios compared to a wide range of temporal and spatio-temporal deep learning models, while offering enhanced interpretability by explicitly modeling cross-stock lead-lag structures. The framework's ability to extract economically meaningful signals directly from raw price-volume data underscores its practical value for quantitative investment.

Highlights

  • 1First end-to-end deep learning framework for discovering dynamic, pair-specific lead-lag patterns in financial markets.
  • 2Novel sparsified cross-attention mechanism that adaptively identifies top-k leading stocks and their optimal lag values on a daily basis.
  • 3Unified detection and prediction stages optimized jointly via a ranking-based loss for cross-sectional stock selection.
  • 4Consistent outperformance over fixed-lag, self-lead-lag, and precomputed statistical lead-lag baselines across multiple US equity markets.
  • 5Superior trading performance and interpretability compared to state-of-the-art temporal and spatio-temporal deep learning models.

Methods

  • M
    Sparsified cross-attention mechanism with temporal encoders (e.g., LSTM) to compute attention scores between target stock queries and candidate leader keys over multiple lags.
  • M
    Top-k selection of lead-lag pairs with attention-weighted aggregation of raw price-volume features from identified leaders.
  • M
    Monotonic logistic ranking loss (log-sum-exp pairwise formulation with tanh smoothing) for optimizing cross-stock return rankings.
  • M
    End-to-end training with joint optimization of lead-lag detection and prediction modules.

Results

  • R
    DeltaLag achieves average annualized returns of 0.247 (S&P 500), 0.333 (NASDAQ), and 0.230 (NYSE) with Sharpe ratios above 2.1 across all markets.
  • R
    Outperforms fixed-lag variant (Lag1Net) by 48-81% in annualized return, confirming the value of dynamic lag learning.
  • R
    Cross-asset modeling yields 31-49% higher annualized returns than self-lead-lag baselines (SelfLagNet, SelfLag1).
  • R
    Adaptive lead-lag detection surpasses precomputed statistical graphs (LagAll CorrGraph, Lag1 CorrGraph, Meta-flow Graph) by 2-10x in annualized return.
  • R
    Outperforms 12 state-of-the-art temporal and spatio-temporal models (e.g., LSTM, Transformer, GNNs) in cumulative returns and Sharpe ratio.
0/5

Analyze Paper

Generate insights from "DeltaLag: Learning Dynamic Lead-Lag Patterns in Financial Ma...".

Suggested Actions