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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

Abstract

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 Jørgensen (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 Søren 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.

Suggested Citation

  • Nielsen, Heino Bohn & Rahbek, Anders, 2007. "The Likelihood Ratio Test For Cointegration Ranks In The I(2) Model," Econometric Theory, Cambridge University Press, vol. 23(4), pages 615-637, August.
    • Handle: RePEc:cup:etheor:v:23:y:2007:i:04:p:615-637_07
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    1. Stillwagon, Josh R., 2015. "Testing the expectations hypothesis with survey forecasts: The impacts of consumer sentiment and the zero lower bound in an I(2) CVAR," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 35(C), pages 85-101.
    2. Jung, Alexander, 2020. "An empirical analysis of loan supply and demand in the euro area," International Review of Economics & Finance, Elsevier, vol. 70(C), pages 187-201.
    3. Jung, Alexander & Carcel Villanova, Hector, 2020. "The empirical properties of euro area M3, 1980-2017," The Quarterly Review of Economics and Finance, Elsevier, vol. 77(C), pages 37-49.
    4. Mihaela Onofrei & Elena Cigu & Anca-Florentina Gavriluta (Vatamanu) & Ionel Bostan & Florin Oprea, 2021. "Effects of the COVID-19 Pandemic on the Budgetary Mechanism Established to Cover Public Health Expenditure. A Case Study of Romania," IJERPH, MDPI, vol. 18(3), pages 1-15, January.
    5. Gomez-Biscarri, Javier & Hualde, Javier, 2015. "A residual-based ADF test for stationary cointegration in I(2) settings," Journal of Econometrics, Elsevier, vol. 184(2), pages 280-294.
    6. Katarina Juselius, 2017. "Using a Theory-Consistent CVAR Scenario to Test an Exchange Rate Model Based on Imperfect Knowledge," Econometrics, MDPI, vol. 5(3), pages 1-20, July.
    7. Kurita, Takamitsu, 2020. "Likelihood-based tests for parameter constancy in I(2) CVAR models with an application to fixed-term deposit data," Journal of Multivariate Analysis, Elsevier, vol. 178(C).
    8. 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.
    9. Andreas Hetland & Simon Hetland, 2017. "Short-Term Expectation Formation Versus Long-Term Equilibrium Conditions: The Danish Housing Market," Econometrics, MDPI, vol. 5(3), pages 1-21, September.
    10. 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.
    11. Frydman Roman & Goldberg Michael D., 2008. "Macroeconomic Theory for a World of Imperfect Knowledge," Capitalism and Society, De Gruyter, vol. 3(3), pages 1-78, December.
    12. Assenmacher-Wesche, Katrin & Beyer, Andreas, 2019. "A cointegration model of money and wealth," CFS Working Paper Series 619, Center for Financial Studies (CFS).
    13. Katarina Juselius & Katrin Assenmacher, 2014. "Real exchange rate persistence: the case of the Swiss franc-US dollar rate," Discussion Papers 14-26, University of Copenhagen. Department of Economics.
    14. Johansen, Søren & Juselius, Katarina & Frydman, Roman & Goldberg, Michael, 2010. "Testing hypotheses in an I(2) model with piecewise linear trends. An analysis of the persistent long swings in the Dmk/$ rate," Journal of Econometrics, Elsevier, vol. 158(1), pages 117-129, September.
    15. 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.
    16. Juselius, Katarina & Stillwagon, Josh R., 2018. "Are outcomes driving expectations or the other way around? An I(2) CVAR analysis of interest rate expectations in the dollar/pound market," Journal of International Money and Finance, Elsevier, vol. 83(C), pages 93-105.
    17. H. Peter Boswijk & Paolo Paruolo, 2017. "Likelihood Ratio Tests of Restrictions on Common Trends Loading Matrices in I(2) VAR Systems," Econometrics, MDPI, vol. 5(3), pages 1-17, June.

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