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

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  • Meier, Alexander
  • Kirch, Claudia
  • Meyer, Renate

Abstract

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.

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  • Meier, Alexander & Kirch, Claudia & Meyer, Renate, 2020. "Bayesian nonparametric analysis of multivariate time series: A matrix Gamma Process approach," Journal of Multivariate Analysis, Elsevier, vol. 175(C).
    • Handle: RePEc:eee:jmvana:v:175:y:2020:i:c:s0047259x18306225
    DOI: 10.1016/j.jmva.2019.104560
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    2. Hu, Zhixiong & Prado, Raquel, 2023. "Fast Bayesian inference on spectral analysis of multivariate stationary time series," Computational Statistics & Data Analysis, Elsevier, vol. 178(C).

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