  In multivariate time series systems, key insights can be obtained by
discovering lead-lag relationships inherent in the data, which refer to the
dependence between two time series shifted in time relative to one another, and
which can be leveraged for the purposes of control, forecasting or clustering.
We develop a clustering-driven methodology for robust detection of lead-lag
relationships in lagged multi-factor models. Within our framework, the
envisioned pipeline takes as input a set of time series, and creates an
enlarged universe of extracted subsequence time series from each input time
series, via a sliding window approach. This is then followed by an application
of 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 are
robustly aggregated to enhance the identification of the consistent
relationships in the original universe. 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 method is not only able to robustly detect
lead-lag relationships in financial markets, but can also yield insightful
results when applied to an environmental data set.
