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Testing for Common Cycles in Non-Stationary VARs with Varied Frequency Data

Thomas B. Götz

Alain Hecq

Jean-Pierre Urbain

VAR Models in Macroeconomics – New Developments and Applications: Essays in Honor of Christopher A. Sims

ISBN: 978-1-78190-752-8

Publication date: 13 December 2013

Abstract

This article proposes a new approach to detecting the presence of common cyclical features when several time series are sampled at different frequencies. We generalize 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 vector error-correction model (VECM) representations extend the results of Ghysels (2012) and are important for determining the correct set of variables to be used in a subsequent common cycle investigation. This fact has implications for the distribution of test statistics and for forecasting. Empirical analyses with quarterly real gross national product (GNP) and monthly industrial production indices for, respectively, the United States and Germany illustrate our new approach. We also conduct a Monte Carlo study which compares our proposed mixed-frequency models with models stemming from classical temporal aggregation methods.

Keywords

Acknowledgements

Acknowledgments

We thank Lutz Kilian, Tom Fomby, and the participants of the 12th Annual Advances in Econometrics Conference in Dallas, the 8th Netherlands Econometric Study Group Meeting in Amsterdam 2013 and the 67th European Meeting of the Econometric Society in Gothenburg 2013 for useful suggestions and comments on earlier versions of the article. The usual disclaimer applies.

Citation

Götz, T.B., Hecq, A. and Urbain, J.-P. (2013), "Testing for Common Cycles in Non-Stationary VARs with Varied Frequency Data", VAR Models in Macroeconomics – New Developments and Applications: Essays in Honor of Christopher A. Sims (Advances in Econometrics, Vol. 32), Emerald Group Publishing Limited, Leeds, pp. 361-393. https://doi.org/10.1108/S0731-9053(2013)0000031010

Publisher

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Emerald Group Publishing Limited