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

In multivariate time series systems, key insights can be obtained by discovering lead-lagrelationships inherent in the data, which refer to the dependence between two timeseries shifted in time relative to one another, and which can be leveraged for thepurposes of control, forecasting or clustering. We develop a clustering-drivenmethodology for robust detection of lead-lag relationships in lagged multi-factormodels. Within our framework, the envisioned pipeline takes as input a set of timeseries, and creates an enlarged universe of extracted subsequence time series fromeach input time series, via a sliding window approach. This is then followed by anapplication of various clustering techniques, (such as k-means++ and spectralclustering), employing a variety of pairwise similarity measures, including nonlinearones. Once the clusters have been extracted, lead-lag estimates across clusters arerobustly aggregated to enhance the identification of the consistent relationships in theoriginal universe. We establish connections to the multireference alignment problem forboth the homogeneous and heterogeneous settings. Since multivariate time series areubiquitous in a wide range of domains, we demonstrate that our method is not onlyable to robustly detect lead-lag relationships in financial markets, but can also yieldinsightful results when applied to an environmental data set