Abstract
This article develops a vector autoregression (VAR) for time series which are observed at mixed frequencies—quarterly and monthly. The model is cast in state-space form and estimated with Bayesian methods under a Minnesota-style prior. We show how to evaluate the marginal data density to implement a data-driven hyperparameter selection. Using a real-time dataset, we evaluate forecasts from the mixed-frequency VAR and compare them to standard quarterly frequency VAR and to forecasts from MIDAS regressions. We document the extent to which information that becomes available within the quarter improves the forecasts in real time. This article has online supplementary materials.
Highlights
In macroeconomic applications, vector autoregressions (VARs) are typically estimated either exclusively based on quarterly observations or exclusively based on monthly observations
The mixed-frequency VAR (MF-VAR) can be conveniently represented as a statespace model, in which the state-transition equations are given by a VAR at monthly frequency and the measurement equations relate the observed series to the underlying, potentially unobserved, monthly variables that are stacked in the state vector
Based on some preliminary exploration of the marginal data density (MDD), we set the number of lags in the state transition of the MF-VAR to p(m) = 6 and the number of lags in the QF-VAR to p(q) = 2
Summary
Vector autoregressions (VARs) are typically estimated either exclusively based on quarterly observations or exclusively based on monthly observations. Giannone, Reichlin, and Small (2008) use a mixed-frequency DFM to evaluate the marginal impact that intra-monthly data releases have on current-quarter forecasts (nowcasts) of real GDP growth. Ghysels, Sinko, and Valkanov (2007) propose a simple univariate regression model, called a mixed data sampling (MIDAS) regression, to exploit high-frequency information without having to estimate a state-space model. Ghysels, and Wright (2013) examine the relationship between MIDAS regressions and state-space models applied to mixed-frequency data They consider dynamic factor models and characterize conditions under which the MIDAS regression exactly replicates the steady state Kalman filter weights on lagged observables. The Online Appendix provides detailed information about the Bayesian computations, the construction of the data set, as well as additional empirical results
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