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Codependence in Cointegrated Autoregressive Models


  • Christoph Schleicher


This paper investigates codependent cycles, i.e. transitory components that react to common stimuli in a similar, although not necessarily synchronous fashion. In a multivariate system, codependence corresponds to an impulse response function that is collinear except for a small number of initial periods. It is shown that the number of cofeature combinations that yield the scalar component models associated with codependence is severely limited by the dimension of a finite-order VAR system. The presence of cointegrating relationships imposes additional cross-equation restrictions and further limits the number of permissible cofeatures. For vector-error correction models, the distribution of FIML based LR tests is therefore different than that of the limited information tests proposed by Vahid and Engle (1997). Monte-Carlo simulations indicate that LR tests yield an increase in power relative to the alternative GMM and canonical correlations tests, while maintaining good size properties. An empirical application investigates the presence of codependence among individual components of the U.S. economy. It is found that the (Beveridge-Nelson) cycle under codepence assumptions contains significantly less high-frequency information than the unconstrained cycle.

Suggested Citation

  • Christoph Schleicher, 2004. "Codependence in Cointegrated Autoregressive Models," Computing in Economics and Finance 2004 286, Society for Computational Economics.
  • Handle: RePEc:sce:scecf4:286

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    References listed on IDEAS

    1. Vahid, F & Engle, Robert F, 1993. "Common Trends and Common Cycles," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 8(4), pages 341-360, Oct.-Dec..
    2. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-1054, July.
    3. Stock, James H & Watson, Mark W, 1988. "Variable Trends in Economic Time Series," Journal of Economic Perspectives, American Economic Association, vol. 2(3), pages 147-174, Summer.
    4. Cubadda, Gianluca & Hecq, Alain, 2001. "On non-contemporaneous short-run co-movements," Economics Letters, Elsevier, vol. 73(3), pages 389-397, December.
    5. Francisco Barillas & Christoph Schleicher, 2003. "Common Trends and Common Cycles in Canadian Sectoral Output," Staff Working Papers 03-44, Bank of Canada.
    6. Engle, Robert F & Kozicki, Sharon, 1993. "Testing for Common Features," Journal of Business & Economic Statistics, American Statistical Association, vol. 11(4), pages 369-380, October.
    7. Engle, Robert F & Kozicki, Sharon, 1993. "Testing for Common Features: Reply," Journal of Business & Economic Statistics, American Statistical Association, vol. 11(4), pages 393-395, October.
    8. Kugler, Peter & Neusser, K, 1993. "International Real Interest Rate Equalization: A Multivariate Time-Series Approach," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 8(2), pages 163-174, April-Jun.
    9. Proietti, Tommaso, 1997. "Short-Run Dynamics in Cointegrated Systems," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 59(3), pages 405-422, August.
    10. Hecq, Alain & Palm, Franz C & Urbain, Jean-Pierre, 2000. " Permanent-Transitory Decomposition in VAR Models with Cointegration and Common Cycles," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 62(4), pages 511-532, September.
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    Cited by:

    1. Trenkler, Carsten & Weber, Enzo, 2012. "Identifying the Shocks behind Business Cycle Asynchrony in Euroland," Working Papers 12-11, University of Mannheim, Department of Economics.
    2. Marco Centoni & Gianluca Cubadda, 2015. "Common Feature Analysis of Economic Time Series: An Overview and Recent Developments," CEIS Research Paper 355, Tor Vergata University, CEIS, revised 05 Oct 2015.
    3. 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).
    4. Franchi, Massimo & Paruolo, Paolo, 2011. "A characterization of vector autoregressive processes with common cyclical features," Journal of Econometrics, Elsevier, vol. 163(1), pages 105-117, July.
    5. repec:eee:econom:v:200:y:2017:i:1:p:118-134 is not listed on IDEAS
    6. Cubadda, Gianluca & Hecq, Alain & Palm, Franz C., 2009. "Studying co-movements in large multivariate data prior to multivariate modelling," Journal of Econometrics, Elsevier, vol. 148(1), pages 25-35, January.
    7. Chen, Xiaoshan & Mills, Terence C., 2009. "Evaluating growth cycle synchronisation in the EU," Economic Modelling, Elsevier, vol. 26(2), pages 342-351, March.
    8. Carsten Trenkler & Enzo Weber, 2013. "Codependent VAR models and the pseudo-structural form," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 97(3), pages 287-295, July.
    9. Marco Centoni & Gianluca Cubadda, 2011. "Modelling comovements of economic time series: a selective survey," Statistica, Department of Statistics, University of Bologna, vol. 71(2), pages 267-294.
    10. Lindenberg, Nannette & Westermann, Frank, 2012. "Common trends and common cycles among interest rates of the G7-countries," Journal of Macroeconomics, Elsevier, vol. 34(4), pages 1125-1140.
    11. Marcel Gorenflo, 2013. "Futures price dynamics of CO 2 emission allowances," Empirical Economics, Springer, vol. 45(3), pages 1025-1047, December.

    More about this item


    vector autoregression; cointegration; business cycles;

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes


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