Testing for Granger causality in large mixed-frequency VARs

In this paper we analyze Granger causality testing in a mixed-frequency VAR, originally proposed by Ghysels (2012), where the difference in sampling frequencies of the variables is large. In particular, we investigate whether past information on a low-frequency variable help in forecasting a high-frequency one and vice versa. 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 two approaches to solve this problem, reduced rank restrictions and a Bayesian mixed-frequency VAR. For the latter, we extend the approach in Banbura et al. (2010) to a mixed-frequency setup, which presents an alternative to classical Bayesian estimation techniques. We compare these methods to a common aggregated low-frequency model as well as to the unrestricted VAR in terms of their Granger non-causality testing behavior using Monte Carlo simulations. The techniques are illustrated in an empirical application involving daily realized volatility and monthly business cycle fluctuations.