Tensor Bayesian Copula Factor Models for High-Dimensional Mixed Time Series Data

We propose a tensor Bayesian copula factor autoregressive model with multivariate responses for analyzing mixed-type time series data with both main effects and interactions. The model is motivated by the need to study dynamic relationships between macroeconomic variables and stock market indices, leading naturally to tensor-valued posterior distributions. Dependence is captured through latent factors in both the multivariate response time series and high-dimensional mixed-type covariates within a quadratic time series regression framework coupled with copula functions. To enhance computational efficiency, we employ a semiparametric extended rank likelihood for the marginal distributions of the covariates, substantially reducing parameter dimensionality. Posterior inference is performed using Metropolis–Hastings and Forward Filtering Backward Sampling algorithms embedded in a Gibbs sampling scheme. The effectiveness of the proposed methodology is demonstrated through extensive simulation studies and an application to a real macroeconomic dataset.

Multivariate tensor time series

Bayesian inference

Factor analysis

Copula models 

Section on Bayesian Statistical Science