On the inconsistency of the unrestricted estimator of the information matrix near a unit root
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 n−1, i.e. a root that takes the form ρ= 1 +c/nα,α≥ 1. In this case the information evaluated at graphic 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.
245-262
Magdalinos, Tassos
ded74727-1ed4-417d-842f-00ea86a3bc31
1 July 2007
Magdalinos, Tassos
ded74727-1ed4-417d-842f-00ea86a3bc31
Magdalinos, Tassos
(2007)
On the inconsistency of the unrestricted estimator of the information matrix near a unit root.
The Econometrics Journal, 10 (2), .
(doi:10.1111/j.1368-423X.2007.00207.x).
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 n−1, i.e. a root that takes the form ρ= 1 +c/nα,α≥ 1. In this case the information evaluated at graphic 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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e-pub ahead of print date: 23 April 2007
Published date: 1 July 2007
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Local EPrints ID: 472216
URI: http://eprints.soton.ac.uk/id/eprint/472216
ISSN: 1368-4221
PURE UUID: 2be73768-e412-40ac-bd3e-b7bcb02820e3
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Date deposited: 29 Nov 2022 17:50
Last modified: 16 Mar 2024 22:40
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