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While there is an increasing amount of literature about Bayesian time series analysis, only a few Bayesian nonparametric approaches to multivariate time series exist. Most methods rely on Whittles Likelihood, involving the second order structure of a stationary time series by means of its spectral density matrix. This is often modeled in terms of the Cholesky decomposition to ensure positive definiteness. However, asymptotic properties such as posterior consistency or posterior contraction rates are not known. A different idea is to model the spectral density matrix by means of random measures. 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. In this work, we present a related approach for multivariate time series, with matrix-valued mixture weights induced by a Hermitian positive definite Gamma process. The proposed procedure is shown to perform well for both simulated and real data. Posterior consistency and contraction rates are also established.
Many modern data sets require inference methods that can estimate the shared and individual-specific components of variability in collections of matrices that change over time. Promising methods have been developed to analyze these types of data in s
The Whittle likelihood is widely used for Bayesian nonparametric estimation of the spectral density of stationary time series. However, the loss of efficiency for non-Gaussian time series can be substantial. On the other hand, parametric methods are
The multivariate Bayesian structural time series (MBSTS) model citep{qiu2018multivariate,Jammalamadaka2019Predicting} as a generalized version of many structural time series models, deals with inference and prediction for multiple correlated time ser
A nonparametric Bayes approach is proposed for the problem of estimating a sparse sequence based on Gaussian random variables. We adopt the popular two-group prior with one component being a point mass at zero, and the other component being a mixture
This paper deals with inference and prediction for multiple correlated time series, where one has also the choice of using a candidate pool of contemporaneous predictors for each target series. Starting with a structural model for the time-series, Ba