  We discuss the issue of estimating large-scale vector autoregressive (VAR)
models with stochastic volatility in real-time situations where data are
sampled at different frequencies. In the case of a large VAR with stochastic
volatility, the mixed-frequency data warrant an additional step in the already
computationally challenging Markov Chain Monte Carlo algorithm used to sample
from the posterior distribution of the parameters. We suggest the use of a
factor stochastic volatility model to capture a time-varying error covariance
structure. Because the factor stochastic volatility model renders the equations
of the VAR conditionally independent, settling for this particular stochastic
volatility model comes with major computational benefits. First, we are able to
improve upon the mixed-frequency simulation smoothing step by leveraging a
univariate and adaptive filtering algorithm. Second, the regression parameters
can be sampled equation-by-equation in parallel. These computational features
of the model alleviate the computational burden and make it possible to move
the mixed-frequency VAR to the high-dimensional regime. We illustrate the model
by an application to US data using our mixed-frequency VAR with 20, 34 and 119
variables.
