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On the Distribution of Likelihood Ratio Test Statistics for Cointegration Rank

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  • Bent Nielsen

Abstract

This paper analyses the likelihood ratio test for the hypothesis of reduced cointegration rank in a Gaussian vector autoregressive model. The usual asymptotic distribution typically gives rather large size distortions. This is explained by the fact that the asymptotic distribution of the likelihood ratio test statistic varies across the parameter space. A much improved distribution approximation can be obtained using local asymptotic theory. The idea is discussed for some low dimensional examples.

Suggested Citation

  • Bent Nielsen, 2004. "On the Distribution of Likelihood Ratio Test Statistics for Cointegration Rank," Econometric Reviews, Taylor & Francis Journals, vol. 23(1), pages 1-23.
    • Handle: RePEc:taf:emetrv:v:23:y:2004:i:1:p:1-23
    DOI: 10.1081/ETC-120028834
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    Citations

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    Cited by:

    1. Carlomagno, Guillermo, 2014. "The pairwise approach to model a large set of disaggregates with common trends," DES - Working Papers. Statistics and Econometrics. WS ws141309, Universidad Carlos III de Madrid. Departamento de Estadística.
    2. Ahlgren, N. & Antell, J., 2008. "Bootstrap and fast double bootstrap tests of cointegration rank with financial time series," Computational Statistics & Data Analysis, Elsevier, vol. 52(10), pages 4754-4767, June.
    3. Giuseppe Cavaliere & Luca Fanelli & Paolo Paruolo, 2009. "Tests for cointegration rank and choice of the alternative," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 18(2), pages 169-191, July.
    4. Bent Nielsen & J. James Reade, 2007. "Simulating Properties of the Likelihood Ratio Test for a Unit Root in an Explosive Second-Order Autoregression," Econometric Reviews, Taylor & Francis Journals, vol. 26(5), pages 487-501.
    5. Noud P.A. van Giersbergen, 2013. "Bartlett correction in the stable second‐order autoregressive model with intercept and trend," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 67(4), pages 482-498, November.
    6. Carlomagno, Guillermo, 2015. "Forecasting a large set of disaggregates with common trends and outliers," DES - Working Papers. Statistics and Econometrics. WS ws1518, Universidad Carlos III de Madrid. Departamento de Estadística.
    7. Marcus J. Chambers, 2015. "A Jackknife Correction to a Test for Cointegration Rank," Econometrics, MDPI, vol. 3(2), pages 1-21, May.
    8. Nielsen, Bent, 2010. "Analysis Of Coexplosive Processes," Econometric Theory, Cambridge University Press, vol. 26(3), pages 882-915, June.
    9. David H. Bernstein & Bent Nielsen, 2019. "Asymptotic Theory for Cointegration Analysis When the Cointegration Rank Is Deficient," Econometrics, MDPI, vol. 7(1), pages 1-24, January.
    10. Paruolo Paolo, 2005. "Design of vector autoregressive processes for invariant statistics," Economics and Quantitative Methods qf0504, Department of Economics, University of Insubria.
    11. Tang, Chor-Foon & Lau, Evan, 2011. "The Behaviour of Disaggregated Public Expenditures and Income in Malaysia," Review of Applied Economics, Lincoln University, Department of Financial and Business Systems, vol. 7(1-2), pages 1-13, March.

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