paperlead-lagdirected-networkhermitian-clusteringflow-imbalanceus-equityml

Bennett, Cucuringu & Reinert (2022) — Lead-Lag Network Clustering

Authors: Stefanos Bennett (Oxford Statistics / Alan Turing Institute), Mihai Cucuringu (Oxford Statistics / Oxford Math Institute / Alan Turing Institute), Gesine Reinert (Oxford Statistics / Alan Turing Institute).

Venue: Machine Learning 111:4497–4538, 2022 (Springer, https://doi.org/10.1007/s10994-022-06250-4). Editor: Joao Gama.

Code: https://github.com/stefanosbennett/mlj-lead-lag

Contribution

First principled methodology for unsupervised clustering of lead-lag clusters in multivariate time series. Pipeline:

  1. Pairwise lead-lag metric S_{ij} from ccf-auc (recommended) or ccf-lag1 or signature (Levin 2016), with corr ∈ {Pearson, Kendall, distance correlation, mutual information}.
  2. Directed network A_{ij} = \max(S_{ij}, 0), clustered by Hermitian RW (Cucuringu 2020) — the first algorithm to directly optimize pairwise flow imbalance.
  3. Meta-flow graph + RowSum leadingness for interpretable "which cluster leads which" ranking.

Validated on 5 synthetic DGP (linear / cosine / Legendre / Hermite / heterogeneous) and on 434 NYSE high-volume stocks 2000-2019. First data-driven lead-lag cluster analysis (previous work only compared against predefined SIC/GICS industry groups).

Downstream trading signal: rolling (2-month update, 1-year lookback) cluster-level EWMA + OLS, meta-flow 90%-thresholded, vol-normalized to 10% annual → annualized Sharpe 0.62, p<0.004 (Opdyke test), market correlation 0.04. LASSO-VAR (5-lag) baseline: 0.27, p>0.13. Random-label permutation test rejects "no lead-lag cluster structure" with p<0.005.

Empirical finding: the data-driven clustering cannot be explained by three prominent lead-lag mechanisms in the empirical finance literature:

  • Sector membership (Biely-Thurner 2008): Jaccard with SIC ~0.15
  • Trading volume (Chordia-Swaminathan 2000): Spearman 0.01
  • Market cap (Lo-MacKinlay 1990): Spearman -0.15

This opens a research direction for novel lead-lag mechanisms (cross-firm information flow, news-driven, microstructure) that current theory does not capture.

Importance to this wiki

Canonical citation for directed-network clustering of lead-lag relationships, complementary to:

Methodologically, the paper bridges Hermitian Spectral Clustering (algorithm) with Lead-Lag Equity Forecasting (application) — the canonical example of "use Hermitian spectrum to find flow-imbalance clusters, then exploit them for prediction".

See also