2018/11/26 by Alexander Meier, Meier, Alexander, Claudia Kirch +3 · 1 citation
Chemistry · Computer Science · Mathematics · #60G57 #62M10 #Bayesian Methods and Mixture Models #FOS: Computer and information sciences #Methodology (stat.ME) #Primary 62G20 #Spectroscopy and Chemometric Analyses #Statistical Methods and Bayesian Inference #secondary 60G15
paper · pdf · doi:10.48550/arxiv.1811.10292
openalex publication_date 2018/11/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
While there is an increasing amount of literature about Bayesian time series\nanalysis, only a few Bayesian nonparametric approaches to multivariate time\nseries exist. Most methods rely on Whittle's Likelihood, involving the second\norder structure of a stationary time series by means of its spectral density\nmatrix. This is often modeled in terms of the Cholesky decomposition to ensure\npositive definiteness. However, asymptotic properties such as posterior\nconsistency or posterior contraction rates are not known. A different idea is\nto model the spectral density matrix by means of random measures. This is in\nline with existing approaches for the univariate case, where the normalized\nspectral density is modeled similar to a probability density, e.g. with a\nDirichlet process mixture of Beta densities. In this work, we present a related\napproach for multivariate time series, with matrix-valued mixture weights\ninduced by a Hermitian positive definite Gamma process. The proposed procedure\nis shown to perform well for both simulated and real data. Posterior\nconsistency and contraction rates are also established.\n