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On the inconsistency of the unrestricted estimator of the information matrix near a unit root

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  • Tassos Magdalinos

Abstract

The unrestricted estimator of the information matrix is shown to be inconsistent for an autoregressive process with a root lying in a neighbourhood of unity with radial length proportional or smaller than 1/n, i.e. a root that takes the form rho=1+c/n^alpha, alpha>=1. In this case the information evaluated at rho-hat_n converges to a non-degenerate random variable and contributes to the asymptotic distribution of a Wald test for the null hypothesis of a random walk versus a stable AR(1) alternative. With this newly derived asymptotic distribution the above Wald test is found to improve its performance. A non local criterion of asymptotic relative efficiency based on Bahadur slopes has been employed for the first time to the problem of unit root testing. The Wald test derived in the paper is found to be as efficient as the Dickey Fuller t ratio test and to outperform the non studentised Dickey Fuller test and a Lagrange Multiplier test.

Suggested Citation

  • Tassos Magdalinos, 2005. "On the inconsistency of the unrestricted estimator of the information matrix near a unit root," Discussion Papers 06/05, University of Nottingham, Granger Centre for Time Series Econometrics.
  • Handle: RePEc:not:notgts:06/05
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    File URL: https://www.nottingham.ac.uk/research/groups/grangercentre/documents/06-05.pdf
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    References listed on IDEAS

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    1. Abadir, Karim M., 1993. "On the Asymptotic Power of Unit Root Tests," Econometric Theory, Cambridge University Press, vol. 9(2), pages 189-221, April.
    2. Abadir, Karim M., 1995. "The Limiting Distribution of the t Ratio Under a Unit Root," Econometric Theory, Cambridge University Press, vol. 11(04), pages 775-793, August.
    3. Liudas Giraitis & Peter C. B. Phillips, 2006. "Uniform Limit Theory for Stationary Autoregression," Journal of Time Series Analysis, Wiley Blackwell, vol. 27(1), pages 51-60, January.
    4. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March.
    5. Phillips, Peter C.B. & Magdalinos, Tassos, 2007. "Limit theory for moderate deviations from a unit root," Journal of Econometrics, Elsevier, vol. 136(1), pages 115-130, January.
    6. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March.
    7. Evans, G B A & Savin, N E, 1981. "Testing for Unit Roots: 1," Econometrica, Econometric Society, vol. 49(3), pages 753-779, May.
    8. Nabeya, Seiji & Tanaka, Katsuto, 1990. "Limiting power of unit-root tests in time-series regression," Journal of Econometrics, Elsevier, vol. 46(3), pages 247-271, December.
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