Adaptive Bayesian Time-Frequency Analysis of Multivariate Time Series

• Published in: Journal of the American Statistical Association Vol. 114; no. 525; pp. 453 - 465
• Main Authors: Li, Zeda, Krafty, Robert T.
• Format: Journal Article
• Language: English
• Published: United States Taylor & Francis 02.01.2019; Taylor & Francis Ltd
• Subjects: Bayesian analysis; Computer simulation; El Nino; Electroencephalography; Empirical analysis; Locally stationary process; Markov analysis; Markov chains; Matrices; Matrix methods; Modified Cholesky decomposition; Monte Carlo simulation; Nonstationary multivariate time series; Oscillation; Partitions; Penalized splines; Power; Power spectrum analysis; Regression analysis; Reversible; Reversible jump Markov chain Monte Carlo; Segments; Simulation; Sleep; Southern Oscillation; Spectra; Spectral analysis; Spectrographic analysis; Spectrum analysis; Statistical methods; Statistics; Time series; Time-frequency analysis; Spectral Analysis; Locally Stationary Process; Modified Cholesky Decomposition; Penalized Splines; Reversible Jump Markov Chain Monte Carlo; Nonstationary Multivariate Time Series
• ISSN: 0162-1459; 1537-274X
• DOI: 10.1080/01621459.2017.1415908

This article introduces a nonparametric approach to multivariate time-varying power spectrum analysis. The procedure adaptively partitions a time series into an unknown number of approximately stationary segments, where some spectral components may remain unchanged across segments, allowing components to evolve differently over time. Local spectra within segments are fit through Whittle likelihood-based penalized spline models of modified Cholesky components, which provide flexible nonparametric estimates that preserve positive definite structures of spectral matrices. The approach is formulated in a Bayesian framework, in which the number and location of partitions are random, and relies on reversible jump Markov chain and Hamiltonian Monte Carlo methods that can adapt to the unknown number of segments and parameters. By averaging over the distribution of partitions, the approach can approximate both abrupt and slowly varying changes in spectral matrices. Empirical performance is evaluated in simulation studies and illustrated through analyses of electroencephalography during sleep and of the El Niño-Southern Oscillation. Supplementary materials for this article are available online.