  Vector autoregressive (VAR) models are popularly adopted for modelling
high-dimensional time series, and their piecewise extensions allow for
structural changes in the data. In VAR modelling, the number of parameters grow
quadratically with the dimensionality which necessitates the sparsity
assumption in high dimensions. However, it is debatable whether such an
assumption is adequate for handling datasets exhibiting strong serial and
cross-sectional correlations. We propose a piecewise stationary time series
model that simultaneously allows for strong correlations as well as structural
changes, where pervasive serial and cross-sectional correlations are accounted
for by a time-varying factor structure, and any remaining idiosyncratic
dependence between the variables is handled by a piecewise stationary VAR
model. We propose an accompanying two-stage data segmentation methodology which
fully addresses the challenges arising from the latency of the component
processes. Its consistency in estimating both the total number and the
locations of the change points in the latent components, is established under
conditions considerably more general than those in the existing literature. We
demonstrate the competitive performance of the proposed methodology on
simulated datasets and an application to US blue chip stocks data.
