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Testing for cointegration in high-dimensional systems



This paper considers cointegration tests for dynamic systems where the number of variables is large relative to the sample size. Typical examples include tests for unit roots in panels, where the units are linked by complicated dynamic relationships. It is well known that conventional cointegration tests based on a parametric (vector autoregressive) representation of the system break down if the number of variables approaches the number of time periods. To sidestep this difficulty we propose nonparametric cointegration tests based on eigenvalue problems that are asymptotically free of nuisance parameters. Furthermore, a nonparametric panel unit root test is suggested. It turns out that if the number of variables is large, the nonparametric tests outperform their parametric (likelihood-ratio based) counterparts by a clear margin.

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  • Jorg Breitung & Gianluca Cubadda, 2009. "Testing for cointegration in high-dimensional systems," CEIS Research Paper 148, Tor Vergata University, CEIS, revised 30 Sep 2009.
  • Handle: RePEc:rtv:ceisrp:148

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    References listed on IDEAS

    1. Shintani, Mototsugu, 2001. "A simple cointegrating rank test without vector autoregression," Journal of Econometrics, Elsevier, vol. 105(2), pages 337-362, December.
    2. MacKinnon, James G & Haug, Alfred A & Michelis, Leo, 1999. "Numerical Distribution Functions of Likelihood Ratio Tests for Cointegration," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 14(5), pages 563-577, Sept.-Oct.
    3. repec:bla:restud:v:57:y:1990:i:1:p:99-125 is not listed on IDEAS
    4. Phillips, Peter C B, 1995. "Fully Modified Least Squares and Vector Autoregression," Econometrica, Econometric Society, vol. 63(5), pages 1023-1078, September.
    5. Moon, H.R.Hyungsik Roger & Perron, Benoit, 2004. "Testing for a unit root in panels with dynamic factors," Journal of Econometrics, Elsevier, vol. 122(1), pages 81-126, September.
    6. M. Hashem Pesaran, 2007. "A simple panel unit root test in the presence of cross-section dependence," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 22(2), pages 265-312.
    7. Hansen, Bruce E., 1992. "Efficient estimation and testing of cointegrating vectors in the presence of deterministic trends," Journal of Econometrics, Elsevier, vol. 53(1-3), pages 87-121.
    8. Martin Wagner, 2008. "On PPP, unit roots and panels," Empirical Economics, Springer, vol. 35(2), pages 229-249, September.
    9. Im, Kyung So & Pesaran, M. Hashem & Shin, Yongcheol, 2003. "Testing for unit roots in heterogeneous panels," Journal of Econometrics, Elsevier, vol. 115(1), pages 53-74, July.
    10. repec:ebl:ecbull:v:3:y:2006:i:17:p:1-7 is not listed on IDEAS
    11. Anindya Banerjee & Massimiliano Marcellino & Chiara Osbat, 2005. "Testing for PPP: Should we use panel methods?," Empirical Economics, Springer, vol. 30(1), pages 77-91, January.
    12. Breuer, Janice Boucher & McNown, Robert & Wallace, Myles, 2002. " Series-Specific Unit Root Tests with Panel Data," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 64(5), pages 527-546, December.
    13. Johansen, Soren, 1991. "Estimation and Hypothesis Testing of Cointegration Vectors in Gaussian Vector Autoregressive Models," Econometrica, Econometric Society, vol. 59(6), pages 1551-1580, November.
    14. Breitung, J rg & Das, Samarjit, 2008. "Testing For Unit Roots In Panels With A Factor Structure," Econometric Theory, Cambridge University Press, vol. 24(01), pages 88-108, February.
    15. Phillips, Peter C B & Ouliaris, S, 1990. "Asymptotic Properties of Residual Based Tests for Cointegration," Econometrica, Econometric Society, vol. 58(1), pages 165-193, January.
    16. Johansen, Soren, 1988. "Statistical analysis of cointegration vectors," Journal of Economic Dynamics and Control, Elsevier, vol. 12(2-3), pages 231-254.
    17. MacKinnon, James G, 1994. "Approximate Asymptotic Distribution Functions for Unit-Root and Cointegration Tests," Journal of Business & Economic Statistics, American Statistical Association, vol. 12(2), pages 167-176, April.
    18. Uwe Hassler, 2006. "A note on Phillips-Perron-type statistics for cointegration testing," Economics Bulletin, AccessEcon, vol. 3(17), pages 1-7.
    19. Breitung, Jorg, 2002. "Nonparametric tests for unit roots and cointegration," Journal of Econometrics, Elsevier, vol. 108(2), pages 343-363, June.
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    Cited by:

    1. Vishal Chandr Jaunky & Robert Lundmark, 2015. "Are Shocks to Wood Fuel Production Permanent? Evidence from the EU," Energies, MDPI, Open Access Journal, vol. 8(11), pages 1-11, November.
    2. Smeekes S. & Urbain J.R.Y.J., 2014. "A multivariate invariance principle for modified wild bootstrap methods with an application to unit root testing," Research Memorandum 008, Maastricht University, Graduate School of Business and Economics (GSBE).

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