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.