Adaptive Bayesian Time–Frequency Analysis of Multivariate Time Series
提出一种非参数方法分析多元时间序列的时变功率谱，自动将序列划分为未知数量的近似平稳段，并允许谱成分在不同段间有不同变化，通过贝叶斯框架和可逆跳跃马尔可夫链蒙特卡洛方法估计，适用于脑电图和厄尔尼诺-南方涛动数据。
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 slow-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.