Dynamic Time Warping for Lead-Lag Relationships in Lagged Multi-Factor Models

ArXiv ID: 2309.08800 “View on arXiv”

Authors: Unknown

Abstract

In multivariate time series systems, lead-lag relationships reveal dependencies between time series when they are shifted in time relative to each other. Uncovering such relationships is valuable in downstream tasks, such as control, forecasting, and clustering. By understanding the temporal dependencies between different time series, one can better comprehend the complex interactions and patterns within the system. We develop a cluster-driven methodology based on dynamic time warping for robust detection of lead-lag relationships in lagged multi-factor models. We establish connections to the multireference alignment problem for both the homogeneous and heterogeneous settings. Since multivariate time series are ubiquitous in a wide range of domains, we demonstrate that our algorithm is able to robustly detect lead-lag relationships in financial markets, which can be subsequently leveraged in trading strategies with significant economic benefits.

Keywords: lead-lag relationships, dynamic time warping, multivariate time series, trading strategies, time series clustering, Financial Markets (General)

Complexity vs Empirical Score

• Math Complexity: 7.5/10
• Empirical Rigor: 6.0/10
• Quadrant: Holy Grail
• Why: The paper presents advanced mathematics including Dynamic Time Warping, multireference alignment connections, and lagged multi-factor models, but also demonstrates robust empirical validation with backtest-ready trading strategies and performance metrics.

  flowchart TD
    A["Research Goal: Detect Lead-Lag Relationships in Multivariate Time Series"] --> B["Input: Multivariate Financial Time Series Data"]
    B --> C["Preprocessing: Stationarity & Alignment"]
    C --> D["Methodology: Dynamic Time Warping DTW<br>with Multireference Alignment MRA"]
    D --> E["Process: Clustering & Temporal Shift Estimation"]
    E --> F["Output: Estimated Lead-Lag Matrices"]
    F --> G["Outcome: Identified Cluster-Level Lead-Lag Structures"]
    G --> H["Application: Trading Strategies<br>Significant Economic Benefits"]