Jackknife bias reduction in the presence of a near-unit root
Jackknife bias reduction in the presence of a near-unit root
This paper considers the specification and performance of jackknife estimators of the autoregressive coefficient in a model with a near-unit root. The limit distributions of sub-sample estimators that are used in the construction of the jackknife estimator are derived, and the joint moment generating function (MGF) of two components of these distributions is obtained and its properties explored. The MGF can be used to derive the weights for an optimal jackknife estimator that removes fully the first-order finite sample bias from the estimator. The resulting jackknife estimator is shown to perform well in finite samples and, with a suitable choice of the number of sub-samples, is shown to reduce the overall finite sample root mean squared error, as well as bias. However, the optimal jackknife weights rely on knowledge of the near-unit root parameter and a quantity that is related to the long-run variance of the disturbance process, which are typically unknown in practice, and so, this dependence is characterised fully and a discussion provided of the issues that arise in practice in the most general settings.
Jackknife , moment generating function, bias reduction, near-unit root
Chambers, Marcus J.
67027b05-b003-4b0a-aea6-b4ef1ee8cdf3
Kyriacou, Maria
6234587e-81f1-4e1d-941d-395996f8bda7
Chambers, Marcus J.
67027b05-b003-4b0a-aea6-b4ef1ee8cdf3
Kyriacou, Maria
6234587e-81f1-4e1d-941d-395996f8bda7
Chambers, Marcus J. and Kyriacou, Maria
(2018)
Jackknife bias reduction in the presence of a near-unit root.
Econometrics, 6 (1), [11].
(doi:10.3390/econometrics6010011).
Abstract
This paper considers the specification and performance of jackknife estimators of the autoregressive coefficient in a model with a near-unit root. The limit distributions of sub-sample estimators that are used in the construction of the jackknife estimator are derived, and the joint moment generating function (MGF) of two components of these distributions is obtained and its properties explored. The MGF can be used to derive the weights for an optimal jackknife estimator that removes fully the first-order finite sample bias from the estimator. The resulting jackknife estimator is shown to perform well in finite samples and, with a suitable choice of the number of sub-samples, is shown to reduce the overall finite sample root mean squared error, as well as bias. However, the optimal jackknife weights rely on knowledge of the near-unit root parameter and a quantity that is related to the long-run variance of the disturbance process, which are typically unknown in practice, and so, this dependence is characterised fully and a discussion provided of the issues that arise in practice in the most general settings.
Text
econometrics-06-00011-v3
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More information
Accepted/In Press date: 22 February 2018
e-pub ahead of print date: 5 March 2018
Additional Information:
Special issue: Celebrated Econometricians: Peter Phillips
Keywords:
Jackknife , moment generating function, bias reduction, near-unit root
Identifiers
Local EPrints ID: 418586
URI: http://eprints.soton.ac.uk/id/eprint/418586
ISSN: 2225-1146
PURE UUID: 7f9d808e-8a72-438c-912b-a7da504c2ce6
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Date deposited: 12 Mar 2018 17:30
Last modified: 15 Mar 2024 18:43
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Author:
Marcus J. Chambers
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