  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.
