On the inconsistency of the unrestricted estimator of the information matrix near a unit root
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.
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Cowles Foundation Discussion Papers
1475, Cowles Foundation for Research in Economics, Yale University.
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- Abadir, Karim M., 1995.
"The Limiting Distribution of the t Ratio Under a Unit Root,"
Cambridge University Press, vol. 11(04), pages 775-793, August.
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- Peter C.B. Phillips & Tassos Magdalinos, 2004.
"Limit Theory for Moderate Deviations from a Unit Root,"
Cowles Foundation Discussion Papers
1471, Cowles Foundation for Research in Economics, Yale University.
- 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.
- Abadir, Karim M., 1993. "On the Asymptotic Power of Unit Root Tests," Econometric Theory, Cambridge University Press, vol. 9(02), pages 189-221, April.
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