IDEAS home Printed from
   My bibliography  Save this paper

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


  • Hecq A.W.
  • Urbain J.R.Y.J.
  • Götz T.B.



This paper proposes a new way for detecting the presence of common cyclical featureswhen several time series are observed/sampled at different frequencies, hence generalizingthe common-frequency approach introduced by Engle and Kozicki 1993 and Vahid andEngle 1993. We start with the mixed-frequency VAR representation investigated in Ghysels2012 for stationary time series. For non-stationary time series in levels, we showthat one has to account for the presence of two sets of long-run relationships. The First setis implied by identities stemming from the fact that the differences of the high-frequencyI1 regressors are stationary. The second set comes from possible additional long-run relationshipsbetween one of the high-frequency series and the low-frequency variables. Ourtransformed VECM representations extend the results of Ghysels 2012 and are very importantfor determining the correct set of variables to be used in a subsequent commoncycle investigation. This has some empirical implications both for the behavior of the teststatistics as well as for forecasting. Empirical analyses with the quarterly real GNP andmonthly industrial production indices for, respectively, the U.S. and Germany illustrate ournew approach. This is also investigated in a Monte Carlo study, where we compare our proposedmixed-frequency models with models stemming from classical temporal aggregationmethods.

Suggested Citation

  • Hecq A.W. & Urbain J.R.Y.J. & Götz T.B., 2013. "Testing for common cycles in non-stationary VARs with varied frecquency data," Research Memorandum 002, Maastricht University, Graduate School of Business and Economics (GSBE).
  • Handle: RePEc:unm:umagsb:2013002

    Download full text from publisher

    File URL:
    Download Restriction: no

    References listed on IDEAS

    1. Andrea Silvestrini & David Veredas, 2008. "Temporal Aggregation Of Univariate And Multivariate Time Series Models: A Survey," Journal of Economic Surveys, Wiley Blackwell, vol. 22(3), pages 458-497, July.
    2. Götz Thomas B. & Hecq Alain & Urbain Jean-Pierre, 2012. "Real-Time Forecast Density Combinations (Forecasting US GDP Growth Using Mixed-Frequency Data)," Research Memorandum 021, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    3. Warne, A., 1993. "A Common Trends Model: Identification, Estimation and Inference," Papers 555, Stockholm - International Economic Studies.
    4. Byeongchan Seong & Sung K. Ahn & Peter A. Zadrozny, 2013. "Estimation of vector error correction models with mixed-frequency data," Journal of Time Series Analysis, Wiley Blackwell, vol. 34(2), pages 194-205, March.
    5. Thomas B. Götz & Alain Hecq & Jean‐Pierre Urbain, 2014. "Forecasting Mixed‐Frequency Time Series with ECM‐MIDAS Models," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 33(3), pages 198-213, April.
    6. Cubadda, Gianluca & Hecq, Alain, 2001. "On non-contemporaneous short-run co-movements," Economics Letters, Elsevier, vol. 73(3), pages 389-397, December.
    7. Hecq, Alain, 1998. "Does seasonal adjustment induce common cycles?," Economics Letters, Elsevier, vol. 59(3), pages 289-297, June.
    8. Zellner, Arnold & Palm, Franz, 1974. "Time series analysis and simultaneous equation econometric models," Journal of Econometrics, Elsevier, vol. 2(1), pages 17-54, May.
    9. Alain Hecq & Franz Palm & Jean-Pierre Urbain, 2001. "Testing for Common Cyclical Features in Var Models with Cointegration," CESifo Working Paper Series 451, CESifo Group Munich.
    10. Zadrozny, Peter, 1988. "Gaussian Likelihood of Continuous-Time ARMAX Models When Data Are Stocks and Flows at Different Frequencies," Econometric Theory, Cambridge University Press, vol. 4(01), pages 108-124, April.
    11. Cubadda Gianluca & Hecq Alain & Palm Franz C., 2007. "Studying Co-movements in Large Multivariate Models Without Multivariate Modelling," Research Memorandum 032, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    12. J. Isaac Miller, 2011. "Cointegrating MiDaS Regressions and a MiDaS Test," Working Papers 1104, Department of Economics, University of Missouri.
    Full references (including those not matched with items on IDEAS)


    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.

    Cited by:

    1. Götz, Thomas B. & Hecq, Alain, 2014. "Nowcasting causality in mixed frequency vector autoregressive models," Economics Letters, Elsevier, vol. 122(1), pages 74-78.
    2. Götz Thomas B. & Hecq Alain & Urbain Jean-Pierre, 2012. "Real-Time Forecast Density Combinations (Forecasting US GDP Growth Using Mixed-Frequency Data)," Research Memorandum 021, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    3. del Barrio Castro, Tomás & Hecq, Alain, 2016. "Testing for deterministic seasonality in mixed-frequency VARs," Economics Letters, Elsevier, vol. 149(C), pages 20-24.
    4. Eric Ghysels & J. Isaac Miller, 2014. "On the Size Distortion from Linearly Interpolating Low-frequency Series for Cointegration Tests," Working Papers 1403, Department of Economics, University of Missouri.
    5. Eric Ghysels & J. Isaac Miller, 2015. "Testing for Cointegration with Temporally Aggregated and Mixed-Frequency Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 36(6), pages 797-816, November.
    6. Marçal, Emerson Fernandes & Zimmermann, Beatrice Aline & Mendonça, Diogo de Prince & Merlin, Giovanni Tondin, 2015. "Does mixed frequency vector error correction model add relevant information to exchange misalignment calculus? Evidence for United States," Textos para discussão 385, FGV/EESP - Escola de Economia de São Paulo, Getulio Vargas Foundation (Brazil).
    7. Götz, Thomas B. & Hecq, Alain & Smeekes, Stephan, 2016. "Testing for Granger causality in large mixed-frequency VARs," Journal of Econometrics, Elsevier, vol. 193(2), pages 418-432.
    8. Ghysels, Eric & Hill, Jonathan B. & Motegi, Kaiji, 2016. "Testing for Granger causality with mixed frequency data," Journal of Econometrics, Elsevier, vol. 192(1), pages 207-230.
    9. John Cotter & Mark Hallam & Kamil Yilmaz, 2017. "Mixed-Frequency Macro-Financial Spillovers," Koç University-TUSIAD Economic Research Forum Working Papers 1704, Koc University-TUSIAD Economic Research Forum.
    10. Götz, Thomas B. & Hecq, Alain & Urbain, Jean-Pierre, 2016. "Combining forecasts from successive data vintages: An application to U.S. growth," International Journal of Forecasting, Elsevier, vol. 32(1), pages 61-74.

    More about this item


    Economic History: Transport; Trade; Energy; Technology; and Other Services: Asia including Middle East; Regional and Urban History: General; Microeconomic Analyses of Economic Development;

    JEL classification:

    • N90 - Economic History - - Regional and Urban History - - - General, International, or Comparative
    • O12 - Economic Development, Innovation, Technological Change, and Growth - - Economic Development - - - Microeconomic Analyses of Economic Development
    • N75 - Economic History - - Economic History: Transport, International and Domestic Trade, Energy, and Other Services - - - Asia including Middle East

    NEP fields

    This paper has been announced in the following NEP Reports:


    Access and download statistics


    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:unm:umagsb:2013002. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Leonne Portz). General contact details of provider: .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.