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

TL;DR

This paper introduces a cluster-driven method using dynamic time warping to detect lead-lag relationships in multivariate time series, with applications demonstrated in financial markets for improved trading strategies.

Contribution

It presents a novel robust detection algorithm for lead-lag relationships in lagged multi-factor models, connecting to multireference alignment problems.

Findings

Effective detection of lead-lag relationships in financial data

Robustness of the method in heterogeneous settings

Potential for economic benefits in trading strategies

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.