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

T.B. Götz, A.W. Hecq, J.R.Y.J. Urbain

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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
Original languageEnglish
Place of PublicationMaastricht
PublisherMaastricht University, Graduate School of Business and Economics
Publication statusPublished - 1 Jan 2013

Publication series

SeriesGSBE Research Memoranda

Cite this

Götz, T. B., Hecq, A. W., & Urbain, J. R. Y. J. (2013). Testing for common cycles in non-stationary VARs with varied frecquency data. Maastricht University, Graduate School of Business and Economics. GSBE Research Memoranda, No. 002 https://doi.org/10.26481/umagsb.2013002