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A Modified Information Criterion For Cointegration Tests Based On A Var Approximation

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  • Qu, Zhongjun
  • Perron, Pierre

Abstract

We consider the cointegration tests of Johansen (1988, Journal of Economic Dynamics and Control 12, 231–254; 1991, Econometrica 59, 1551–1580) when a vector autoregressive (VAR) process of order k is used to approximate a more general linear process with a possibly infinite VAR representation. Traditional methods to select the lag order, such as Akaike's information criterion (AIC) or the Bayesian information criterion, often lead to too parsimonious a model with the implication that the cointegration tests suffer from substantial size distortions in finite samples. We extend the analysis of Ng and Perron (2001, Econometrica 69, 1519–1554) to derive a modified Akaike's information criterion (MAIC) in this multivariate setting. The idea is to use the information specified by the null hypothesis as it relates to restrictions on the parameters of the model to keep an extra term in the penalty function of the AIC. This MAIC takes a very simple form for which this extra term is simply the likelihood ratio test for testing the null hypothesis of r against more than r cointegrating vectors. We provide theoretical analyses of its validity and of the fact that cointegration tests constructed from a VAR whose lag order is selected using the MAIC have the same limit distribution as when the order is finite and known. We also provide theoretical and simulation analyses to show how the MAIC leads to VAR approximations that yield tests with drastically improved size properties with little loss of power.We are grateful to two referees for especially useful and constructive comments.

Suggested Citation

  • Qu, Zhongjun & Perron, Pierre, 2007. "A Modified Information Criterion For Cointegration Tests Based On A Var Approximation," Econometric Theory, Cambridge University Press, vol. 23(4), pages 638-685, August.
    • Handle: RePEc:cup:etheor:v:23:y:2007:i:04:p:638-685_07
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    Cited by:

    1. Tu, Yundong & Yi, Yanping, 2017. "Forecasting cointegrated nonstationary time series with time-varying variance," Journal of Econometrics, Elsevier, vol. 196(1), pages 83-98.
    2. Yan Qian & Zijun Wang, 2021. "A model selection approach to jointly testing for structural breaks and cointegration with application to the Eurocurrency interest rates market," Empirical Economics, Springer, vol. 61(2), pages 799-825, August.
    3. Matteo Barigozzi & Giuseppe Cavaliere & Lorenzo Trapani, 2024. "Inference in Heavy-Tailed Nonstationary Multivariate Time Series," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 119(545), pages 565-581, January.
    4. Antonia Arsova, 2019. "Exchange rate pass-through to import prices in Europe: A panel cointegration approach," Working Paper Series in Economics 384, University of Lüneburg, Institute of Economics.
    5. Kascha, Christian & Trenkler, Carsten, 2011. "Bootstrapping the likelihood ratio cointegration test in error correction models with unknown lag order," Computational Statistics & Data Analysis, Elsevier, vol. 55(2), pages 1008-1017, February.
    6. Giorgio Mattei & Barbara Pistoresi, 2019. "Unemployment and suicide in Italy: evidence of a long-run association mitigated by public unemployment spending," The European Journal of Health Economics, Springer;Deutsche Gesellschaft für Gesundheitsökonomie (DGGÖ), vol. 20(4), pages 569-577, June.
    7. Harris, David & Leybourne, Stephen J. & Taylor, A.M. Robert, 2016. "Tests of the co-integration rank in VAR models in the presence of a possible break in trend at an unknown point," Journal of Econometrics, Elsevier, vol. 192(2), pages 451-467.
    8. Arsova, Antonia & Karaman Örsal, Deniz Dilan, 2021. "A panel cointegrating rank test with structural breaks and cross-sectional dependence," Econometrics and Statistics, Elsevier, vol. 17(C), pages 107-129.
    9. Marco Morales, 2014. "Cointegration testing under structural change: reducing size distortions and improving power of residual based tests," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 23(2), pages 265-282, June.
    10. Carrion-i-Silvestre Josep Lluis & Surdeanu Laura, 2011. "Panel Cointegration Rank Testing with Cross-Section Dependence," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 15(4), pages 1-43, September.
    11. Fossati, Sebastian, 2012. "Covariate unit root tests with good size and power," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3070-3079.
    12. Antonia Arsova, 2021. "Exchange rate pass-through to import prices in Europe: a panel cointegration approach," Empirical Economics, Springer, vol. 61(1), pages 61-100, July.
    13. Makram El-Shagi, 2011. "An evolutionary algorithm for the estimation of threshold vector error correction models," International Economics and Economic Policy, Springer, vol. 8(4), pages 341-362, December.
    14. Bauer, Dietmar & Wagner, Martin, 2009. "Using subspace algorithm cointegration analysis: Simulation performance and application to the term structure," Computational Statistics & Data Analysis, Elsevier, vol. 53(6), pages 1954-1973, April.

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