Factor Modelling for Clustering High-dimensional Time Series

TL;DR

This paper introduces an unsupervised clustering method for high-dimensional time series using a latent factor model, allowing for flexible cluster structures and unclustered series, with proven consistency and practical demonstrations.

Contribution

It develops a novel factor-based clustering approach for high-dimensional time series, including theoretical guarantees and real-world applications.

Findings

Consistent estimation of factors and clusters with explicit convergence rates

Effective clustering demonstrated on simulated and real data

Advances statistical inference for existing factor models

Abstract

We propose a new unsupervised learning method for clustering a large number of time series based on a latent factor structure. Each cluster is characterized by its own cluster-specific factors in addition to some common factors which impact on all the time series concerned. Our setting also offers the flexibility that some time series may not belong to any clusters. The consistency with explicit convergence rates is established for the estimation of the common factors, the cluster-specific factors, the latent clusters. Numerical illustration with both simulated data as well as a real data example is also reported. As a spin-off, the proposed new approach also advances significantly the statistical inference for the factor model of Lam and Yao (2012).