Adaptive Bayesian Spectral Analysis of High-dimensional Nonstationary Time Series

TL;DR

This paper presents a Bayesian nonparametric spectral analysis method for high-dimensional nonstationary time series, capable of adaptively detecting spectral changes and segmenting the series into stationary parts.

Contribution

It introduces a novel frequency-domain factor model with Bayesian shrinkage priors and uses SAMC for adaptive segmentation, advancing spectral analysis of complex multivariate data.

Findings

Effective in modeling abrupt and gradual spectral changes

Demonstrated superior performance on simulated data

Successfully applied to high-density EEG analysis

Abstract

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.