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Simulating properties of the likelihood ratio test for a unit root in an explosive second order autoregression


  • Bent Nielsen

    () (Nuffield College, Oxford University, UK)

  • J. James Reade

    (St. Cross College, University of Oxford)


This paper provides a means of accurately simulating explosive autoregressive processes, and uses this method to analyse the distribution of the likelihood ratio test statistic for an explosive second order autoregressive process. Nielsen (2001) has shown that for the asymptotic distribution of the likelihood ratio unit root test statistic in a higher order autoregressive model, the assumption that the remaining roots are stationary is unnecessary, and as such the approximating asymptotic distribution for the test in the difference stationary region is valid in the explosive region also. However, simulations of statistics in the explosive region are beset by the magnitude of the numbers involved, which cause numerical inaccuracies, and this has previously constituted a bar on supporting asymptotic results by means of simulation, and analysing the finite sample properties of tests in the explosive region.

Suggested Citation

  • Bent Nielsen & J. James Reade, 2004. "Simulating properties of the likelihood ratio test for a unit root in an explosive second order autoregression," Economics Papers 2004-W24, Economics Group, Nuffield College, University of Oxford.
  • Handle: RePEc:nuf:econwp:0424

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    1. Bent Nielsen, 1995. "Bartlett correction of the unit root test in autoregressive models," Economics Papers 11 & 98., Economics Group, Nuffield College, University of Oxford.
    2. Nielsen, Bent, 2001. "The Asymptotic Distribution of Unit Root Tests of Unstable Autoregressive Processes," Econometrica, Econometric Society, vol. 69(1), pages 211-219, January.
    3. 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.
    4. Nielsen, Bent, 2005. "Strong Consistency Results For Least Squares Estimators In General Vector Autoregressions With Deterministic Terms," Econometric Theory, Cambridge University Press, vol. 21(03), pages 534-561, June.
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