  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).
