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The Likelihood Ratio Test For Cointegration Ranks In The I(2) Model


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  • Nielsen, Heino Bohn
  • Rahbek, Anders


This paper presents the likelihood ratio (LR) test for the number of cointegrating relations in the I(2) vector autoregressive model. It is shown that the asymptotic distribution of the LR test for the cointegration ranks is identical to the asymptotic distribution of the much applied test statistic based on the two-step estimation procedure in Johansen (1995, Econometric Theory 11, 25 59), Paruolo (1996, Journal of Econometrics 72, 313 356), and Rahbek, Kongsted, and J rgensen (1999, Journal of Econometrics 90, 265 289). By construction the LR test statistic is smaller than the non-LR test statistic from the two-step procedure, and application of the LR test may change rank selection in empirical work. Based on a study of existing empirical applications and related Monte Carlo simulations we conclude that the LR test has much better size properties when compared to the two-step-based test. Overall, we propose use of the LR test for rank determination in I(2) analysis.Discussions with S ren Johansen, Hans Christian Kongsted, and Bent Nielsen are gratefully acknowledged. We also thank the editor and three anonymous referees for very constructive comments that have led to a much improved version of the paper. This research was supported by Danish Social Sciences Research Council grant 2114-04-0001.

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Bibliographic Info

Article provided by Cambridge University Press in its journal Econometric Theory.

Volume (Year): 23 (2007)
Issue (Month): 04 (August)
Pages: 615-637

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Handle: RePEc:cup:etheor:v:23:y:2007:i:04:p:615-637_07

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Cited by:
  1. Søren Johansen & Katarina Juselius & Roman Frydman & Michael Goldberg, 2007. "Testing Hypotheses in an I(2) Model with Applications to the Persistent Long Swings in the Dmk/$ Rate," Discussion Papers 07-34, University of Copenhagen. Department of Economics.
  2. Heino Nielsen & Christopher Bowdler, 2006. "Inflation adjustment in the open economy: an I(2) analysis of UK prices," Empirical Economics, Springer, vol. 31(3), pages 569-586, September.
  3. Takamitsu Kurita, 2009. "A note on testing parameter constancy in cointegrated vector autoregression: the case of near I(2) processes," Economics Bulletin, AccessEcon, vol. 29(2), pages 575-587.


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