Testing for Granger Causality in Large Mixed-Frequency VARs

We analyze Granger causality testing in a mixed-frequency VAR, where the difference in sampling frequencies of the variables is large. Given a realistic sample size, the number of high-frequency observations per low-frequency period leads to parameter proliferation problems in case we attempt to estimate the model unrestrictedly. We propose several tests based on reduced rank restrictions, and implement bootstrap versions to account for the uncertainty when estimating factors and to improve the finite sample properties of these tests. We also consider a Bayesian VAR that we carefully extend to the presence of mixed frequencies. We compare these methods to an aggregated model, the max-test approach introduced by Ghysels et al. (2015a) as well as to the unrestricted VAR using Monte Carlo simulations. The techniques are illustrated in an empirical application involving daily realized volatility and monthly business cycle fluctuations.