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In multivariate time series systems, key insights can be obtained bydiscovering lead-lag relationships inherent in the data, which refer to thedependence between two time series shifted in time relative to one another, andwhich can be leveraged for the purposes of control, forecasting or clustering.We develop a clustering-driven methodology for robust detection of lead-lagrelationships in lagged multi-factor models. Within our framework, theenvisioned pipeline takes as input a set of time series, and creates anenlarged universe of extracted subsequence time series from each input timeseries, via a sliding window approach. This is then followed by an applicationof various clustering techniques, (such as k-means++ and spectral clustering),employing a variety of pairwise similarity measures, including nonlinear ones.Once the clusters have been extracted, lead-lag estimates across clusters arerobustly aggregated to enhance the identification of the consistentrelationships in the original universe. We establish connections to themultireference alignment problem for both the homogeneous and heterogeneoussettings. Since multivariate time series are ubiquitous in a wide range ofdomains, we demonstrate that our method is not only able to robustly detectlead-lag relationships in financial markets, but can also yield insightfulresults when applied to an environmental data set.

Robust Detection of Lead-Lag Relationships in Lagged Multi-Factor Models