  This article introduces a nonparametric approach to spectral analysis of a
high-dimensional multivariate nonstationary time series. The procedure is based
on a novel frequency-domain factor model that provides a flexible yet
parsimonious representation of spectral matrices from a large number of
simultaneously observed time series. Real and imaginary parts of the factor
loading matrices are modeled independently using a prior that is formulated
from the tensor product of penalized splines and multiplicative gamma process
shrinkage priors, allowing for infinitely many factors with loadings
increasingly shrunk towards zero as the column index increases. Formulated in a
fully Bayesian framework, the time series is adaptively partitioned into
approximately stationary segments, where both the number and location of
partition points are assumed unknown. Stochastic approximation Monte Carlo
(SAMC) techniques are used to accommodate the unknown number of segments, and a
conditional Whittle likelihood-based Gibbs sampler is developed for efficient
sampling within segments. By averaging over the distribution of partitions, the
proposed method can approximate both abrupt and slowly varying changes in
spectral matrices. Performance of the proposed model is evaluated by extensive
simulations and demonstrated through the analysis of high-density
electroencephalography.
