Clustering High-Dimensional Time Series Based on Parallelism

This article considers the problem of clustering high-dimensional time series based on trend parallelism. The underlying process is modeled as a nonparametric trend function contaminated by locally stationary errors, a special class of nonstationary processes. For each group where the parallelism holds, I semiparametrically estimate its representative trend function and vertical shifts of group members, and establish their central limit theorems. An information criterion, consisting of in-group similarities and number of groups, is then proposed for the purpose of clustering. I prove its theoretical consistency and propose a splitting-coalescence algorithm to reduce the computational burden in practice. The method is illustrated by both simulation and a real-data example.