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The Problem of Co-integration


  • Josef Artl


This paper is concerned with the problem of multiple time series modelling under the condition of nonstationarity in means. It is well known that the economic time series are characteristic by nonstationary development. In the univariate case this problem is solved very simply, just by differencing. But in the multivariate case the differencing is not an effective way how to get rid of nonstationarity in means because of co-integration which can occure. If the co-integration between some time series does exists and is not respected it usually leads to the incorrect model of the multivariate time series. This model has to be transformed into a restricted form which is called the error correction model. The problem of co-integration and error correction model is relatively new. The relationship between co-integration and error correction models was first suggested by C.W.J. Granger (1981). A theorem showing precisely that co-integration series can be represented by error correction models was originally stated and proved in Granger (1983). This theorem was than presented in Engle, Granger (1987) under the name 'Granger Representation Theorem'. These articles were than followed by many other papers, especially concerning the testing of co-integration and the estimating of error correction models.

Suggested Citation

  • Josef Artl, 1995. "The Problem of Co-integration," Bulletin of the Czech Econometric Society, The Czech Econometric Society, vol. 2(2).
  • Handle: RePEc:czx:journl:v:2:y:1995:i:2:id:18

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    References listed on IDEAS

    1. Dirk Tasche, 2004. "The single risk factor approach to capital charges in case of correlated loss given default rates," Papers cond-mat/0402390,, revised Feb 2004.
    2. Konstantin Belyaev & Aelita Belyaeva & Tomas Konecny & Jakub Seidler & Martin Vojtek, 2012. "Macroeconomic Factors as Drivers of LGD Prediction: Empirical Evidence from the Czech Republic," Working Papers 2012/12, Czech National Bank, Research Department.
    3. Acharya, Viral V. & Bharath, Sreedhar T. & Srinivasan, Anand, 2007. "Does industry-wide distress affect defaulted firms? Evidence from creditor recoveries," Journal of Financial Economics, Elsevier, vol. 85(3), pages 787-821, September.
    4. Jiri Witzany, 2011. "A Two Factor Model for PD and LGD Correlation," Bulletin of the Czech Econometric Society, The Czech Econometric Society, vol. 18(28).
    5. Jon Frye, 2000. "Depressing recoveries," Emerging Issues, Federal Reserve Bank of Chicago, issue Oct.
    6. Stefano Caselli & Stefano Gatti & Francesca Querci, 2008. "The Sensitivity of the Loss Given Default Rate to Systematic Risk: New Empirical Evidence on Bank Loans," Journal of Financial Services Research, Springer;Western Finance Association, vol. 34(1), pages 1-34, August.
    7. Seidler, Jakub & Horvath, Roman & JakubĂ­k, Petr, 2009. "Estimating expected loss given default in an emerging market: the case of Czech Republic," Journal of Financial Transformation, Capco Institute, vol. 27, pages 103-107.
    8. De Graeve, F. & Kick, T. & Koetter, M., 2008. "Monetary policy and financial (in)stability: An integrated micro-macro approach," Journal of Financial Stability, Elsevier, vol. 4(3), pages 205-231, September.
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