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

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  • Paruolo Paolo

    (Department of Economics, University of Insubria, Italy)

Abstract

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.

Suggested Citation

  • Paruolo Paolo, 2002. "Testing for common trends in conditional I(2) VAR models," Economics and Quantitative Methods qf0216, Department of Economics, University of Insubria.
    • Handle: RePEc:ins:quaeco:qf0216
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    File URL: https://www.eco.uninsubria.it/RePEc/pdf/QF2002_28.pdf
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    References listed on IDEAS

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    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. Cubadda, Gianluca, 1999. "Common Cycles in Seasonal Non-stationary Time Series," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 14(3), pages 273-291, May-June.
    3. Johansen, Søren, 1995. "A Stastistical Analysis of Cointegration for I(2) Variables," Econometric Theory, Cambridge University Press, vol. 11(1), pages 25-59, February.
    4. Paruolo, Paolo, 1996. "On the determination of integration indices in I(2) systems," Journal of Econometrics, Elsevier, vol. 72(1-2), pages 313-356.
    5. Cubadda, Gianluca & Hecq, Alain, 2001. "On non-contemporaneous short-run co-movements," Economics Letters, Elsevier, vol. 73(3), pages 389-397, December.
    6. David F. Hendry & Hans-Martin Krolzig, 2005. "The Properties of Automatic "GETS" Modelling," Economic Journal, Royal Economic Society, vol. 115(502), pages 32-61, March.
    7. Paruolo, Paolo, 2002. "Asymptotic Inference On The Moving Average Impact Matrix In Cointegrated I (2) Var Systems," Econometric Theory, Cambridge University Press, vol. 18(3), pages 673-690, June.
    8. repec:cup:etheor:v:8:y:1992:i:2:p:188-202 is not listed on IDEAS
    9. Vahid, Farshid & Engle, Robert F., 1997. "Codependent cycles," Journal of Econometrics, Elsevier, vol. 80(2), pages 199-221, October.
    10. Omtzigt, Pieter & Paruolo, Paolo, 2005. "Impact factors," Journal of Econometrics, Elsevier, vol. 128(1), pages 31-68, September.
    11. 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.
    12. Stock, James H & Watson, Mark W, 1993. "A Simple Estimator of Cointegrating Vectors in Higher Order Integrated Systems," Econometrica, Econometric Society, vol. 61(4), pages 783-820, July.
    13. 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.
    14. Paruolo, Paolo & Rahbek, Anders, 1999. "Weak exogeneity in I(2) VAR systems," Journal of Econometrics, Elsevier, vol. 93(2), pages 281-308, December.
    15. 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.
    16. 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.
    17. 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.
    18. 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.
    19. Kitamura, Yuichi, 1995. "Estimation of Cointegrated Systems with I(2) Processes," Econometric Theory, Cambridge University Press, vol. 11(1), pages 1-24, February.
    20. Alain Hecq & Franz Palm & Jean-Pierre Urbain, 2001. "Testing for Common Cyclical Features in Var Models with Cointegration," CESifo Working Paper Series 451, CESifo.
    21. Paruolo, Paolo, 2000. "Asymptotic Efficiency Of The Two Stage Estimator In I (2) Systems," Econometric Theory, Cambridge University Press, vol. 16(4), pages 524-550, August.
    22. Johansen, Søren, 1992. "A Representation of Vector Autoregressive Processes Integrated of Order 2," Econometric Theory, Cambridge University Press, vol. 8(2), pages 188-202, June.
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    1. Paruolo, Paolo, 2006. "Common trends and cycles in I(2) VAR systems," Journal of Econometrics, Elsevier, vol. 132(1), pages 143-168, May.
    2. Omtzigt, Pieter & Paruolo, Paolo, 2005. "Impact factors," Journal of Econometrics, Elsevier, vol. 128(1), pages 31-68, September.

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    Keywords

    cointegration rank test; common trends; VAR; I(2); 2SI2; conditional systems;
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