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Jackknife bias reduction in the presence of a near-unit root

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 are 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, which is typically unknown in practice, and so an alternative, feasible, jackknife estimator is proposed which achieves the intended bias reduction but does not rely on knowledge of this parameter. This feasible jackknife estimator is also capable of substantial bias and root mean squared error reductions in finite samples across a range of values of the near-unit root parameter and across different sample sizes.
University of Essex
Chambers, Marcus J.
6591c606-5ed7-409f-a741-77d1a13e9c39
Kyriacou, Maria
6234587e-81f1-4e1d-941d-395996f8bda7
Chambers, Marcus J.
6591c606-5ed7-409f-a741-77d1a13e9c39
Kyriacou, Maria
6234587e-81f1-4e1d-941d-395996f8bda7

Chambers, Marcus J. and Kyriacou, Maria (2016) Jackknife bias reduction in the presence of a near-unit root (University of Essex, Economics Discussion Papers) Colchester, GB. University of Essex 35pp.

Record type: Monograph (Discussion Paper)

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 are 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, which is typically unknown in practice, and so an alternative, feasible, jackknife estimator is proposed which achieves the intended bias reduction but does not rely on knowledge of this parameter. This feasible jackknife estimator is also capable of substantial bias and root mean squared error reductions in finite samples across a range of values of the near-unit root parameter and across different sample sizes.

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Published date: 23 September 2016
Organisations: Economics

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Local EPrints ID: 400745
URI: http://eprints.soton.ac.uk/id/eprint/400745
PURE UUID: 8e1b9fbc-7aeb-4107-ba06-6b84c1f08596

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Date deposited: 26 Sep 2016 08:59
Last modified: 13 Jun 2018 16:31

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