Adaptive Bayesian Factor Spectral Analysis of High--Dimensional Nonstationary Time Series

• Activity Number: 352 - Recent Development in Imaging Data Analysis
• Type: Contributed
• Date/Time: Tuesday, July 30, 2019 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistics in Imaging
• Author(s): Zeda Li* and Rob Krafty and Ori Rosen
• Companies: Baruch College CUNY and University of Pittsburgh and University of Texas at El Paso
• Keywords: Time Series; Factor Analysis; Spectral Analysis; Bayesian Nonparametric; Locally Stationary Process

Abstract

We introduce a nonparametric approach for the time-varying power spectrum analysis of high-dimensional multivariate 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 using tensor products of penalized splines and multiplicative gamma process shrinkage priors, allowing for possibly infinite 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 random. Stochastic approximation Monte Carlo (SAMC) techniques are used to adapt to the unknown number of segments and a conditional Whittle likelihood-based Gibbs sampler is developed for efficient model fitting within segments. By averaging over the distribution of partitions, the approach can approximate both abrupt and slowly varying changes in spectral matrices.