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

Abstract

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.

Keywords: High-dimensional time series, Lead-lag relationships, Unsupervised learning, Clustering, Financial markets

JEL Classification: C1, G1