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

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

Stefanos Bennett
Mihai Cucuringu
Gesine Reinert
Published on 1/20/2022
Equities
United States (US)
Stocks
Machine learning
Momentum
Stock picking
Market timing

This paper introduces a novel unsupervised method for detecting lead-lag clusters in multivariate time series, applied to US equity data. The method constructs a directed network from pairwise lead-lag metrics, then applies Hermitian clustering to identify clusters with high flow imbalance. The authors evaluate several lead-lag metrics (e.g., cross-correlation functionals and signatures) and clustering algorithms on synthetic data, finding that Hermitian clustering with Pearson ccf-auc performs best. On US equity data, the method uncovers statistically significant clusters that align with industry sectors and market capitalization, with large-cap stocks leading small-cap stocks. A trading signal based on cluster leadingness generates significant out-of-sample returns, demonstrating practical applicability. The work is the first to provide data-driven clustering of lead-lag networks in finance and shows promise for forecasting in noisy, high-dimensional settings.

Highlights

  • 1First unsupervised clustering method for lead-lag relationships in multivariate time series, validated on synthetic and real data.
  • 2Novel evaluation of pairwise lead-lag metrics using a new benchmark data generating process with clustered lead-lag structure.
  • 3First data-driven clustering of lead-lag networks in a financial market context, applied to US equities.
  • 4Construction of a statistically significant trading signal from lead-lag clusters, demonstrating practical utility for forecasting.

Methods

  • M
    Pairwise lead-lag metrics based on functionals of cross-correlation (Pearson, Kendall, distance correlation, mutual information) with ccf-lag1 and ccf-auc aggregation.
  • M
    Signature-based lead-lag metric from rough path theory using second-order iterated integrals.
  • M
    Directed network clustering algorithms: Hermitian clustering (Cucuringu et al., 2020), DI-SIM co-clustering, bibliometric symmetrization, and naive symmetrization.
  • M
    Leadingness metric based on row-sum ranking of the skew-symmetric lead-lag matrix to order clusters by leadership.

Results

  • R
    Hermitian clustering with Pearson ccf-auc metric best recovers ground-truth clusters in synthetic experiments.
  • R
    Statistically significant lead-lag clusters detected in US equity market, with clusters corresponding to industry sectors and market capitalization.
  • R
    Clusters exhibit persistent lead-lag structure over time, with larger-cap stocks tending to lead smaller-cap stocks.
  • R
    Trading strategy based on cluster leadingness yields significant out-of-sample returns, demonstrating predictive value.
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