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

Testing for common cycles in non-stationary VARs with varied frecquency data

This paper proposes a new way for detecting the presence of common cyclical features when several time series are observed/sampled at different frequencies, hence generalizing the common-frequency approach introduced by Engle and Kozicki (1993) and Vahid and Engle (1993). We start with the mixed-frequency VAR representation investigated in Ghysels (2012) for stationary time series. For non-stationary time series in levels, we show that one has to account for the presence of two sets of long-run relationships. The First set is implied by identities stemming from the fact that the differences of the high-frequency I(1) regressors are stationary. The second set comes from possible additional long-run relationships between one of the high-frequency series and the low-frequency variables. Our transformed VECM representations extend the results of Ghysels (2012) and are very important for determining the correct set of variables to be used in a subsequent common cycle investigation. This has some empirical implications both for the behavior of the test statistics as well as for forecasting. Empirical analyses with the quarterly real GNP and monthly industrial production indices for, respectively, the U.S. and Germany illustrate our new approach. This is also investigated in a Monte Carlo study, where we compare our proposed mixed-frequency models with models stemming from classical temporal aggregation methods

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

Nowcasting causality in mixed frequency vector autoregressive models

This paper introduces the notion of nowcasting causality for mixed-frequency VARs as the mixed-frequency version of instantaneous causality. We analyze the relationship between nowcasting and Granger causality in the mixed-frequency VAR setting of Ghysels (2012) and illustrate that nowcasting causality can have a crucial impact on the significance of contemporaneous or lagged high-frequency variables in standard MIDAS regression models

Combining forecasts from successive data vintages: An application to U.S. growth

We extend the repeated observations forecasting analysis of Stark and Croushore (2002) to allow for regressors that may be of higher sampling frequencies than the regressand. For the U.S. GNP quarterly growth rate, we compare the forecasting performances of an autoregressive model with those of several mixed-frequency models, including the MIDAS approach. Using the additional dimension provided by different vintages, we compute several forecasts for a given calendar date with each model, then approximate the corresponding distribution of forecasts by a continuous density. Next, we combine these model-specific densities using scoring rules and analyze both the composition and the evolution of the implied weights over time. In so doing, not only do we investigate the sensitivity of model selection to the choice of which data release to consider, we also illustrate how revision process information can be incorporated into real time studies. As a consequence of these analyses, we introduce a new weighting scheme that summarizes the information contained in the revision process of the variables under consideration