Bayesian nonparametric analysis of multivariate time series: A matrix Gamma Process approach

JOURNAL OF MULTIVARIATE ANALYSIS

卷:175

Article

Meier, Alexander¹  Kirch, Claudia²  Meyer, Renate³ 

[1] Otto von Guericke Univ, Dept Math, Inst Math Stochast, Magdeburg, Germany

[2] Otto von Guericke Univ, Dept Math, Inst Math Stochast, Ctr Behav Brain Sci, Magdeburg, Germany

[3] Univ Auckland, Dept Stat, Auckland, New Zealand

关键词: Bayesian nonparametrics completely;    random measures;    Spectral density;    Stationary multivariate time series;   

DOI  :  10.1016/j.jmva.2019.104560

来源: Elsevier

【 摘 要 】

Many Bayesian nonparametric approaches to multivariate time series rely on Whittle's Likelihood, involving the second order structure of a stationary time series by means of its spectral density matrix. In this work, we model the spectral density matrix by means of random measures that are constructed in such a way that positive definiteness is ensured. This is in line with existing approaches for the univariate case, where the normalized spectral density is modeled similar to a probability density, e.g. with a Dirichlet process mixture of Beta densities. We present a related approach for multivariate time series, with matrix-valued mixture weights induced by a Hermitian positive definite Gamma process. The latter has not been considered in the literature, allows to include prior knowledge and possesses a series representation that will be used in MCMC methods. We establish posterior consistency and contraction rates and small sample performance of the proposed procedure is shown in a simulation study and for real data. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free