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Testing hypotheses in an I(2) model with applications to the persistent long swings in the Dmk/$ rate

  • Søren Johansen
  • Katarina Juselius
  • Roman Frydberg
  • Michael Goldberg


    (School of Economics and Management, University of Aarhus, Denmark and CREATES)

This paper discusses a number of likelihood ratio tests on long-run relations and common trends in the I(2) model and provide new results on the test of overidentifying restrictions on beta’xt and the asymptotic variance for the stochastic trends parameters, alpha 1: How to specify deterministic components in the I(2) model is discussed at some length. Model specification and tests are illustrated with an empirical analysis of long and persistent swings in the foreign exchange market between Germany and USA. The data analyzed consist of nominal exchange rates, relative prices, US in.ation rate, two long-term interest rates and two short-term interest rates over the 1975-1999 period. One important aim of the paper is to demonstrate that by structuring the data with the help of the I(2) model one can achieve a better understanding of the empirical regularities underlying the persistent swings in nominal exchange rates, typical in periods of floating exchange rates.

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Paper provided by School of Economics and Management, University of Aarhus in its series CREATES Research Papers with number 2008-03.

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Length: 33
Date of creation: 15 Jan 2008
Date of revision:
Handle: RePEc:aah:create:2008-03
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  1. Dornbusch, Rudiger & Frankel, Jeffrey, 1988. "The Flexible Exchange Rate System: Experience and Alternatives," Department of Economics, Working Paper Series qt5ct1w459, Department of Economics, Institute for Business and Economic Research, UC Berkeley.
  2. Boswijk, H. Peter, 2000. "Mixed Normality And Ancillarity In I(2) Systems," Econometric Theory, Cambridge University Press, vol. 16(06), pages 878-904, December.
  3. Frédérique Bec & Anders Rahbek, 2004. "Vector equilibrium correction models with non-linear discontinuous adjustments," Econometrics Journal, Royal Economic Society, vol. 7(2), pages 628-651, December.
  4. Nielsen, Heino Bohn & Rahbek, Anders, 2007. "The Likelihood Ratio Test For Cointegration Ranks In The I(2) Model," Econometric Theory, Cambridge University Press, vol. 23(04), pages 615-637, August.
  5. Dornbusch, Rudiger, 1976. "Expectations and Exchange Rate Dynamics," Journal of Political Economy, University of Chicago Press, vol. 84(6), pages 1161-76, December.
  6. Heino Bohn Nielsen, 2004. "Cointegration analysis in the presence of outliers," Econometrics Journal, Royal Economic Society, vol. 7(1), pages 249-271, 06.
  7. Luca Fanelli & Emanuele Bacchiocchi, 2005. "Testing the purchasing power parity through I(2) cointegration techniques," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 20(6), pages 749-770.
  8. Gonzalo, Jesus, 1994. "Five alternative methods of estimating long-run equilibrium relationships," Journal of Econometrics, Elsevier, vol. 60(1-2), pages 203-233.
  9. Juselius, Katarina, 2006. "The Cointegrated VAR Model: Methodology and Applications," OUP Catalogue, Oxford University Press, number 9780199285679, July.
  10. Clara Jørgensen & Hans Christian Kongsted & Anders Rahbek, 1996. "Trend-Stationarity in the I(2) Cointegration Model," Discussion Papers 96-12, University of Copenhagen. Department of Economics.
  11. Paruolo, Paolo, 1997. "Asymptotic Inference on the Moving Average Impact Matrix in Cointegrated 1(1) VAR Systems," Econometric Theory, Cambridge University Press, vol. 13(01), pages 79-118, February.
  12. Johansen, Soren, 1995. "Likelihood-Based Inference in Cointegrated Vector Autoregressive Models," OUP Catalogue, Oxford University Press, number 9780198774501, July.
  13. repec:cup:etheor:v:23:y:2007:i:04:p:615-637 is not listed on IDEAS
  14. Nielsen, Bent & Rahbek, Anders, 2000. " Similarity Issues in Cointegration Analysis," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 62(1), pages 5-22, February.
  15. Paruolo, Paolo & Rahbek, Anders, 1999. "Weak exogeneity in I(2) VAR systems," Journal of Econometrics, Elsevier, vol. 93(2), pages 281-308, December.
  16. Paruolo, Paolo, 2000. "Asymptotic Efficiency Of The Two Stage Estimator In I (2) Systems," Econometric Theory, Cambridge University Press, vol. 16(04), pages 524-550, August.
  17. Johansen, Søren, 1992. "A Representation of Vector Autoregressive Processes Integrated of Order 2," Econometric Theory, Cambridge University Press, vol. 8(02), pages 188-202, June.
  18. Kongsted, Hans Christian, 2005. "Testing the nominal-to-real transformation," Journal of Econometrics, Elsevier, vol. 124(2), pages 205-225, February.
  19. Henrik Hansen & Søren Johansen, 1999. "Some tests for parameter constancy in cointegrated VAR-models," Econometrics Journal, Royal Economic Society, vol. 2(2), pages 306-333.
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