Likelihood Ratio Testing for Cointegration Ranks in I(2) Models

Heino Bohn Nielsen and Anders Rahbek
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Heino Bohn Nielsen: University of Copenhagen, Institute of Economics

No 03-42, Discussion Papers from University of Copenhagen. Department of Economics

Abstract: This paper presents the likelihood ratio (LR) test for the number of cointegrating and multi-cointegrating relations in the I(2) vector autoregressive model. It is shown that the asymptotic distribution of the LR test for the (multi-) cointegration ranks is identical to the asymptotic distribution of the much applied test statistic based on the Two-Step procedure in Johansen (1995), Paruolo (1996), and Rahbek, Kongsted, and Jørgensen (1999). By construction the LR test statistic is smaller than the non-LR test statistic from the Two-Step procedure as the latter ignores some of the restrictions concerning the hypothesis of I(2), 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 to use of the LR test for rank determination in I(2) analysis as the Two-Step based statistic was developed as a feasible approximation to the then unobtainable LR test.

Keywords: vector autoregression; error correction model; cointegration; I(2); likelihood ratio test; Monte Carlo; reduced rank; rank testing (search for similar items in EconPapers)
JEL-codes: C32 (search for similar items in EconPapers)
Pages: 25 pages
Date: 2003-12
New Economics Papers: this item is included in nep-ecm and nep-ets
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Citations: View citations in EconPapers (3)

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