Bayesian estimation of large dimensional time varying VARs using copulas

TL;DR

This paper introduces a novel Bayesian method for estimating large, time-varying VAR models by decomposing the multivariate problem into univariate estimations linked via copulas, simplifying computation and handling high-dimensional data.

Contribution

The paper proposes a new approach that treats each variable's equation separately and combines them with copulas, enabling efficient estimation of large, time-varying VARs.

Findings

Method successfully applied to a 25-variable macroeconomic dataset.

Estimation process is parallelizable and computationally efficient.

Provides reliable joint posterior inference for high-dimensional models.

Abstract

This paper provides a simple, yet reliable, alternative to the (Bayesian) estimation of large multivariate VARs with time variation in the conditional mean equations and/or in the covariance structure. With our new methodology, the original multivariate, n dimensional model is treated as a set of n univariate estimation problems, and cross-dependence is handled through the use of a copula. Thus, only univariate distribution functions are needed when estimating the individual equations, which are often available in closed form, and easy to handle with MCMC (or other techniques). Estimation is carried out in parallel for the individual equations. Thereafter, the individual posteriors are combined with the copula, so obtaining a joint posterior which can be easily resampled. We illustrate our approach by applying it to a large time-varying parameter VAR with 25 macroeconomic variables.