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Jackknife bias reduction in autoregressive models with a unit root

Jackknife bias reduction in autoregressive models with a unit root
Jackknife bias reduction in autoregressive models with a unit root
This paper is concerned with the application of jackknife methods as a means of bias reduction in the estimation of autoregressive models with a unit root. It is shown that the usual jackknife estimator based on non-overlapping sub-samples does not remove fully the first-order bias as intended, but that an ‘optimal’ jackknife estimator can be defined that is capable of removing this bias. The results are based on a demonstration that the sub-sample estimators converge to different limiting distributions, and the joint moment generating function of the numerator and denominator of these distributions (which are functionals of a Wiener process over a sub-interval of [0,1]) is derived and utilised to extract the optimal weights. Simulations demonstrate the ability of the jackknife estimator to produce substantial bias reductions in the parameter of interest. It is also shown that incorporating an intercept in the regressions allows the standard jackknife estimator to be used and it is able also to produce substantial bias reduction despite the fact that the distributions of the full-sample and sub-sample estimators have greater bias in this case. Of interest, too, is the fact that the jackknife estimators can also reduce the overall root mean squared error compared to the ordinary least squares estimator, this requiring a larger (though still small) number of sub-samples compared to the value that produces maximum bias reduction (which is typically equal to two).
jackknife, bias reduction, unit root, moment generating function
WP–CEA–02-2012
Cass Business School
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 (2012) Jackknife bias reduction in autoregressive models with a unit root (CEA@Cass Working Paper Series, WP–CEA–02-2012) London, GB. Cass Business School 29pp.

Record type: Monograph (Working Paper)

Abstract

This paper is concerned with the application of jackknife methods as a means of bias reduction in the estimation of autoregressive models with a unit root. It is shown that the usual jackknife estimator based on non-overlapping sub-samples does not remove fully the first-order bias as intended, but that an ‘optimal’ jackknife estimator can be defined that is capable of removing this bias. The results are based on a demonstration that the sub-sample estimators converge to different limiting distributions, and the joint moment generating function of the numerator and denominator of these distributions (which are functionals of a Wiener process over a sub-interval of [0,1]) is derived and utilised to extract the optimal weights. Simulations demonstrate the ability of the jackknife estimator to produce substantial bias reductions in the parameter of interest. It is also shown that incorporating an intercept in the regressions allows the standard jackknife estimator to be used and it is able also to produce substantial bias reduction despite the fact that the distributions of the full-sample and sub-sample estimators have greater bias in this case. Of interest, too, is the fact that the jackknife estimators can also reduce the overall root mean squared error compared to the ordinary least squares estimator, this requiring a larger (though still small) number of sub-samples compared to the value that produces maximum bias reduction (which is typically equal to two).

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More information

Published date: February 2012
Keywords: jackknife, bias reduction, unit root, moment generating function
Organisations: Economics

Identifiers

Local EPrints ID: 300402
URI: http://eprints.soton.ac.uk/id/eprint/300402
PURE UUID: cd1f6e53-fe49-461e-8461-746e2326c527
ORCID for Maria Kyriacou: ORCID iD orcid.org/0000-0001-7996-2015

Catalogue record

Date deposited: 22 Feb 2012 11:51
Last modified: 14 Mar 2024 10:24

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Contributors

Author: Marcus J. Chambers
Author: Maria Kyriacou ORCID iD

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