Hostname: page-component-78c5997874-mlc7c Total loading time: 0 Render date: 2024-11-09T13:57:11.707Z Has data issue: false hasContentIssue false
  • English
  • Français

THE LIKELIHOOD RATIO TEST FOR COINTEGRATION RANKS IN THE I(2) MODEL

Published online by Cambridge University Press:  25 April 2007

Heino Bohn Nielsen  and
Anders Rahbek
Heino Bohn Nielsen
Affiliation:
University of Copenhagen
Anders Rahbek
Affiliation:
University of Copenhagen
Get access Rights & Permissions [Opens in a new window]

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.

Type
Research Article
Information
Econometric Theory , Volume 23 , Issue 4 , August 2007 , pp. 615 - 637
Copyright
© 2007 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Bacchiocchi, E. & L. Fanelli (2005) Testing the purchasing power parity through I(2) cointegration techniques. Journal of Applied Econometrics 20, 749–770.Google Scholar
Banerjee, A., L. Cockerell, & B. Russell (2001) An I(2) analysis of inflation and the markup. Journal of Applied Econometrics 16, 221–240.Google Scholar
Banerjee, A. & B. Russell (2001) The relationship between the markup and inflation in the G7 economies and Australia. Review of Economics and Statistics 83, 377–387.Google Scholar
Boswijk, H.P. (2000) Mixed normality and ancillarity in I(2) systems. Econometric Theory 16, 878–904.Google Scholar
Dennis, J. (2006) CATS in RATS—Cointegration Analysis of Time Series, Version 2. Estima.
Diamandis, P., D. Georgoutsos, & G. Kouretas (2000) The monetary model in the presence of I(2) components: Long-run relationships, short-run dynamics and forecasting of the Greek drachma. Journal of International Money and Finance 19, 917–941.Google Scholar
Doornik, J.A. (1998) Approximations to the asymptotic distribution of cointegration tests. Journal of Economic Surveys 12, 573–593.Google Scholar
Fliess, N. & R. MacDonald (2001) The instability of the money demand function: An I(2) interpretation. Oxford Bulletin of Economics and Statistics 63, 475–495.Google Scholar
Haldrup, N. (1998) A review of the econometric analysis of I(2) variables. Journal of Economic Surveys 12, 595–650.Google Scholar
Johansen, S. (1992) A representation of vector autoregressive processes integrated of order 2. Econometric Theory 8, 188–202.Google Scholar
Johansen, S. (1995) A statistical analysis of cointegration for I(2) variables. Econometric Theory 11, 25–59.Google Scholar
Johansen, S. (1997) Likelihood analysis of the I(2) model. Scandinavian Journal of Statistics 24, 433–462.Google Scholar
Johansen, S. (2002) A small sample correction for the test of cointegration rank in the vector autoregressive model. Econometrica 70, 1929–1961.Google Scholar
Johansen, S. (2006) Statistical analysis of hypotheses on the cointegrating relations in the I(2) model. Journal of Econometrics 132, 81–115.Google Scholar
Juselius, K. (1998) A structured VAR for Denmark under changing monetary regimes. Journal of Business & Economic Statistics 16, 400–412.Google Scholar
Juselius, K. (1999) Price convergence in the medium and long run: An I(2) analysis of six price indices. In R.F. Engle & H. White (eds.), Cointegration, Causality, and Forecasting—A Festschrift in Honour of Clive W.J. Granger. Oxford University Press.
Kongsted, H.C. (2003) An I(2) cointegration analysis of small-country import price determination. Econometrics Journal 6, 53–71.Google Scholar
Kurita, T. (2006) Likelihood Analysis of Weak Exogeneity in I(2) Systems and Reduced Econometric Representations. Working paper, Nuffield College, Oxford.
Nielsen, B. & A. Rahbek (2000) Similarity issues in cointegration analysis. Oxford Bulletin of Economics and Statistics 62, 5–22.Google Scholar
Nielsen, H.B. (2002) An I(2) cointegration analysis of price and quantity formation in Danish manufactured exports. Oxford Bulletin of Economics and Statistics 64, 449–472.Google Scholar
Paruolo, P. (1996) On the determination of integration indices in I(2) systems. Journal of Econometrics 72, 313–356.Google Scholar
Paruolo, P. (2000) Asymptotic efficiency of the two stage estimator in I(2) systems. Econometric Theory 16, 524–550.Google Scholar
Paruolo, P. & A. Rahbek (1999) Weak exogeneity in I(2) VAR systems. Journal of Econometrics 93, 281–308.Google Scholar
Rahbek, A., H.C. Kongsted, & C. Jørgensen (1999) Trend-stationarity in the I(2) cointegration model. Journal of Econometrics 90, 265–289.Google Scholar
Rahbek, A. & H.B. Nielsen (2006) Likelihood Analysis of the I(2) Cointegration Model with Trend Stationarity. Working paper, University of Copenhagen.