# Lead-lag detection and network clustering for multivariate time series with an application to the US equity market

arXiv: https://arxiv.org/abs/2201.08283 · HTML: https://mlsanity.com/paper/2201.08283/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 89 references that are in the map.
- First posted on arXiv 20 Jan 2022.

## Builds on (most cited first, 15 of 15)

- [From Louvain to Leiden: guaranteeing well-connected communities](https://mlsanity.com/paper/1810.08473/) (2018)
- [Detecting causal associations in large nonlinear time series datasets](https://mlsanity.com/paper/1702.07007/) (2017)
- [A Primer on the Signature Method in Machine Learning](https://mlsanity.com/paper/1603.03788/) (2016)
- [Granger Causality: A Review and Recent Advances](https://mlsanity.com/paper/2105.02675/) (2021)
- [The iisignature library: efficient calculation of iterated-integral signatures and log signatures](https://mlsanity.com/paper/1802.08252/) (2018)
- [The Impact of Random Models on Clustering Similarity](https://mlsanity.com/paper/1701.06508/) (2017)
- [Hermitian matrices for clustering directed graphs: insights and applications](https://mlsanity.com/paper/1908.02096/) (2019)
- [Higher-Order Spectral Clustering of Directed Graphs](https://mlsanity.com/paper/2011.05080/) (2020)
- [A Survey and Taxonomy of Graph Sampling](https://mlsanity.com/paper/1308.5865/) (2013)
- [A physical model for efficient ranking in networks](https://mlsanity.com/paper/1709.09002/) (2017)
- [Spectral Ranking using Seriation](https://mlsanity.com/paper/1406.5370/) (2014)
- [Ranking and synchronization from pairwise measurements via SVD](https://mlsanity.com/paper/1906.02746/) (2019)
- [Spectral Ranking with Covariates](https://mlsanity.com/paper/2005.04035/) (2020)
- [Motif-Based Spectral Clustering of Weighted Directed Networks](https://mlsanity.com/paper/2004.01293/) (2020)
- [Exploring and measuring non-linear correlations: Copulas, Lightspeed Transportation and Clustering](https://mlsanity.com/paper/1610.09659/) (2016)

## Built on by (most cited first, 11 of 11)

- [Efficient Integration of Multi-Order Dynamics and Internal Dynamics in Stock Movement Prediction](https://mlsanity.com/paper/2211.07400/) (2022)
- [A Shapelet-based Framework for Unsupervised Multivariate Time Series Representation Learning](https://mlsanity.com/paper/2305.18888/) (2023)
- [Explaining Preferences with Shapley Values](https://mlsanity.com/paper/2205.13662/) (2022)
- [Graph similarity learning for change-point detection in dynamic networks](https://mlsanity.com/paper/2203.15470/) (2022)
- [TimeCSL: Unsupervised Contrastive Learning of General Shapelets for Explorable Time Series Analysis](https://mlsanity.com/paper/2404.05057/) (2024)
- [Robust Detection of Lead-Lag Relationships in Lagged Multi-Factor Models](https://mlsanity.com/paper/2305.06704/) (2023)
- [Stable and Interpretable Deep Learning for Tabular Data: Introducing InterpreTabNet with the Novel InterpreStability Metric](https://mlsanity.com/paper/2310.02870/) (2023)
- [Spectral Clustering for Directed Graphs via Likelihood Estimation on Stochastic Block Models](https://mlsanity.com/paper/2403.19516/) (2024)
- [Online Sparsification of Bipartite-Like Clusters in Graphs](https://mlsanity.com/paper/2508.05437/) (2025)
- [ChorusTIC: Training-Free Multivariate Time Series Classification via Chorus In-Context Learning](https://mlsanity.com/paper/2608.24033/) (2026)
- [Say, Echo, Do: Strategic Narratives and Revealed Positioning in Financial Markets](https://mlsanity.com/paper/2609.38545/) (2026)

## Abstract (arXiv)

In multivariate time series systems, it has been observed that certain groups of variables partially lead the evolution of the system, while other variables follow this evolution with a time delay; the result is a lead-lag structure amongst the time series variables. In this paper, we propose a method for the detection of lead-lag clusters of time series in multivariate systems. We demonstrate that the web of pairwise lead-lag relationships between time series can be helpfully construed as a directed network, for which there exist suitable algorithms for the detection of pairs of lead-lag clusters with high pairwise imbalance. Within our framework, we consider a number of choices for the pairwise lead-lag metric and directed network clustering components. Our framework is validated on both a synthetic generative model for multivariate lead-lag time series systems and daily real-world US equity prices data. We showcase that our method is able to detect statistically significant lead-lag clusters in the US equity market. We study the nature of these clusters in the context of the empirical finance literature on lead-lag relations and demonstrate how these can be used for the construction of predictive financial signals.