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Testing for common trends in conditional I(2) VAR models

  • Paruolo Paolo


    (Department of Economics, University of Insubria, Italy)

This paper presents cointegration tests in the integration indices (II) in cointegrated (CI) vector autoregressive processes (VAR). The statistical analysis is performed under the assumption that some variables are weakly exogenous with respect to the (multi-)cointegration parameters, a condition that corresponds to no integral and proportional feedback in the marginal system (NF). The specification of the deterministic components is chosen so as to allow for a linear trend in all possible directions.The asymptotic distribution is derived both under correct specification of the weak exogeneity assumptions and under mis-specification. Tables of limit distributions are obtained by simulation. It is found that some types of mis-specification modify the asymptotic distributions of the tests considerably. However, the asymptotics are unaffected by misspecification provided the adjustment coefficients in the conditional system are of full rank.

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Paper provided by Department of Economics, University of Insubria in its series Economics and Quantitative Methods with number qf0216.

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Length: 40 pages
Date of creation: Dec 2002
Date of revision:
Handle: RePEc:ins:quaeco:qf0216
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  1. Johansen, S., 1991. "A Statistical Analsysis of Cointegration for I(2) Variables," Papers 77, Helsinki - Department of Economics.
  2. James H. Stock & Mark W. Watson, 1991. "A simple estimator of cointegrating vectors in higher order integrated systems," Working Paper Series, Macroeconomic Issues 91-3, Federal Reserve Bank of Chicago.
  3. Omtzigt Pieter & Paruolo Paolo, 2002. "Impact factors," Economics and Quantitative Methods qf0203, Department of Economics, University of Insubria.
  4. 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.
  5. David Hendry & Hans-Martin Krolzig, 2003. "The Properties of Automatic Gets Modelling," Economics Papers 2003-W14, Economics Group, Nuffield College, University of Oxford.
  6. 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 163-74, April-Jun.
  7. 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.
  8. Cubadda, Gianluca, 1999. "Common Cycles in Seasonal Non-stationary Time Series," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 14(3), pages 273-91, May-June.
  9. 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.
  10. Engle, Robert F & Kozicki, Sharon, 1993. "Testing for Common Features," Journal of Business & Economic Statistics, American Statistical Association, vol. 11(4), pages 369-80, October.
  11. 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.
  12. Vahid, F & Engle, Robert F, 1993. "Common Trends and Common Cycles," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 8(4), pages 341-60, Oct.-Dec..
  13. Vahid, Farshid & Engle, Robert F., 1997. "Codependent cycles," Journal of Econometrics, Elsevier, vol. 80(2), pages 199-221, October.
  14. Gouriéroux, Christian & Peaucelle, Irina, 1992. "Séries codépendantes : application à l’hypothèse de parité du pouvoir d’achat," L'Actualité Economique, Société Canadienne de Science Economique, vol. 68(1), pages 283-304, mars et j.
  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. Alain Hecq & Franz Palm & Jean-Pierre Urbain, 2002. "Separation, Weak Exogeneity, And P-T Decomposition In Cointegrated Var Systems With Common Features," Econometric Reviews, Taylor & Francis Journals, vol. 21(3), pages 273-307.
  17. Gianluca Cubadda, 2001. "Common Features In Time Series With Both Deterministic And Stochastic Seasonality," Econometric Reviews, Taylor & Francis Journals, vol. 20(2), pages 201-216.
  18. Rahbek, Anders & Christian Kongsted, Hans & Jorgensen, Clara, 1999. "Trend stationarity in the I(2) cointegration model," Journal of Econometrics, Elsevier, vol. 90(2), pages 265-289, June.
  19. Paruolo, Paolo, 1996. "On the determination of integration indices in I(2) systems," Journal of Econometrics, Elsevier, vol. 72(1-2), pages 313-356.
  20. Kitamura, Yuichi, 1995. "Estimation of Cointegrated Systems with I(2) Processes," Econometric Theory, Cambridge University Press, vol. 11(01), pages 1-24, February.
  21. repec:cup:etheor:v:8:y:1992:i:2:p:188-202 is not listed on IDEAS
  22. Cubadda, Gianluca & Hecq, Alain, 2001. "On non-contemporaneous short-run co-movements," Economics Letters, Elsevier, vol. 73(3), pages 389-397, December.
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