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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"Uniform Limit Theory for Stationary Autoregression,"
Cowles Foundation Discussion Papers
1475, Cowles Foundation for Research in Economics, Yale University.
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Journal of Econometrics,
Elsevier, vol. 136(1), pages 115-130, January.
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"The Limiting Distribution of the T Ratio Under a Unit Root,"
1992-2, American Cairo - Economics and Political Sciences.
- 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.
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