Point and Density Forecasts Using an Unrestricted Mixed-Frequency VAR Model

Abstract

This paper compares the forecasting performance of the unrestricted mixed-frequency VAR (MF-VAR) model to the more commonly used VAR (LF-VAR) model sampled a common low-frequency. The literature so far has successfully documented the forecast gains that can be obtained from using high-frequency variables in forecasting a lower frequency variable in a univariate mixed-frequency setting. These forecast gains are usually attributed to the ability of the mixed-frequency models to nowcast. More recently, Ghysels (2014) provides an approach that allows the usage of mixed-frequency variables in a VAR framework. In this paper we assess the forecasting and nowcasting performance of the MF-VAR of Ghysels (2014), however, we do not impose any restrictions on the parameters of the models. Although the unrestricted version is more flexible, it suffers from parameter proliferation and is therefore only suitable when the difference between the low- and high-frequency variables is small (i.e. quarterly and monthly frequencies). Unlike previous work, our interest is not only limited to evaluating the out-of-sample performance in terms of point forecasts but also density forecasts. Thus, we suggest a parametric bootstrap approach as well as a Bayesian approach to compute density forecasts. Moreover, we show how the nowcasts can be obtained using both direct and iterative forecasting methods. We use both Monte Carlo simulation experiments and an empirical study for the US to compare the forecasting performance of both the MF-VAR model and the LF-VAR model. The results highlight the point and density forecasts gains that can be achieved by the MF-VAR model.