Factor Modeling for Clustering High-Dimensional Time Series

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, and 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. for this article are available online.

Automated summary

We propose a new unsupervised learning method for clustering time series based on a latent factor structure, where each cluster has its own specific factors and common factors that impact all the time series. The estimation of the common factors, cluster-specific factors, and latent clusters is shown to have explicit convergence rates. Numerical illustrations using simulated and real data are provided, and the proposed approach also advances statistical inference for the factor model of Lam and Yao.