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

A common-feature approach for testing present-value restrictions with financial data

It is well known that cointegration between the level of two variables (labeled Yt and yt in this paper) is a necessary condition to assess the empirical validity of a present-value model (PV and PVM, respectively, hereafter) linking them. The work on cointegration has been so prevalent that it is often overlooked that another necessary condition for the PVM to hold is that the forecast error entailed by the model is orthogonal to the past. The basis of this result is the use of rational expectations in forecasting future values of variables in the PVM. If this condition fails, the present-value equation will not be valid, since it will contain an additional term capturing the (non-zero) conditional expected value of future error terms. Our article has a few novel contributions, but two stand out. First, in testing for PVMs, we advise to split the restrictions implied by PV relationships into orthogonality conditions (or reduced rank restrictions) before additional tests on the value of parameters. We show that PV relationships entail a weak-form common feature relationship as in Hecq, Palm, and Urbain (2006) and in Athanasopoulos, Guillén, Issler and Vahid (2011) and also a polynomial serial-correlation common feature relationship as in Cubadda and Hecq (2001), which represent restrictions on dynamic models which allow several tests for the existence of PV relationships to be used. Because these relationships occur mostly with nancial data, we propose tests based on generalized method of moment (GMM) estimates, where it is straightforward to propose robust tests in the presence of heteroskedasticity. We also propose a robust Wald test developed to investigate the presence of reduced rank models. Their performance is evaluated in a Monte-Carlo exercise. Second, in the context of asset pricing, we propose applying a permanent-transitory (PT) decomposition based on Beveridge and Nelson (1981), which focus on extracting the long-run component of asset prices, a key concept in modern nancial theory as discussed in Alvarez and Jermann (2005), Hansen and Scheinkman (2009), and Nieuwerburgh, Lustig, Verdelhan (2010). Here again we can exploit the results developed in the common cycle literature to easily extract permament and transitory components under both long and also short-run restrictions. The techniques discussed herein are applied to long span annual data on long- and short-term interest rates and on price and dividend for the U.S. economy. In both applications we do not reject the existence of a common cyclical feature vector linking these two series. Extracting the long-run component shows the usefulness of our approach and highlights the presence of asset-pricing bubbles

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

Combining distributions of real-time forecasts: An application to U.S. growth

We extend the repeated observations forecasting (ROF) analysis of Croushore and Stark (2002) to allow for regressors of possibly higher sampling frequencies than the regressand. For the U.S. GNP quarterly growth rate, we compare the forecasting performances of an AR model with several mixed-frequency models among which is the MIDAS approach. Using the additional dimension provided by different vintages we compute several forecasts for a given calendar date and subsequently approximate the corresponding distribution of forecasts by a continuous density. Scoring rules are then employed to construct combinations of them and analyze the composition and evolvement of the implied weights over time. Using this approach, we not only investigate the sensitivity of model selection to the choice of which data release to consider, but also illustrate how to incorporate revision process information into real-time studies. As a consequence of these analyses, we introduce a new weighting scheme that summarizes information contained in the revision process of the variables under consideration