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Testing for cointegration in high-dimensional systems

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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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Bibliographic Info

Paper provided by Tor Vergata University, CEIS in its series CEIS Research Paper with number 148.

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Length: 27 pages
Date of creation: 30 Sep 2009
Date of revision: 30 Sep 2009
Handle: RePEc:rtv:ceisrp:148

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Postal: CEIS - Centre for Economic and International Studies - Faculty of Economics - University of Rome "Tor Vergata" - Via Columbia, 2 00133 Roma
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  1. repec:ebl:ecbull:v:3:y:2006:i:17:p:1-7 is not listed on IDEAS
  2. 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.
  3. Wagner, Martin, 2005. "On PPP, Unit Roots and Panels," Economics Series 176, Institute for Advanced Studies.
  4. Uwe Hassler, 2006. "A note on Phillips-Perron-type statistics for cointegration testing," Economics Bulletin, AccessEcon, vol. 3(17), pages 1-7.
  5. 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 563-77, Sept.-Oct.
  6. 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.
  7. Breitung, Jorg, 2002. "Nonparametric tests for unit roots and cointegration," Journal of Econometrics, Elsevier, vol. 108(2), pages 343-363, June.
  8. 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 167-76, April.
  9. 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.
  10. Phillips, Peter C B, 1995. "Fully Modified Least Squares and Vector Autoregression," Econometrica, Econometric Society, vol. 63(5), pages 1023-78, September.
  11. Mototsugu Shintani, 2000. "A Simple Cointegrating Rank Test Without Vector Autoregression," Vanderbilt University Department of Economics Working Papers 0044, Vanderbilt University Department of Economics.
  12. 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.
  13. Johansen, Soren, 1988. "Statistical analysis of cointegration vectors," Journal of Economic Dynamics and Control, Elsevier, vol. 12(2-3), pages 231-254.
  14. Phillips, Peter C B & Ouliaris, S, 1990. "Asymptotic Properties of Residual Based Tests for Cointegration," Econometrica, Econometric Society, vol. 58(1), pages 165-93, January.
  15. 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 527-46, December.
  16. 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.
  17. Johansen, Soren, 1991. "Estimation and Hypothesis Testing of Cointegration Vectors in Gaussian Vector Autoregressive Models," Econometrica, Econometric Society, vol. 59(6), pages 1551-80, November.
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