Jackknife bias reduction in the presence of a unit root
Jackknife bias reduction in the presence of a unit root
This paper analyses the properties of jackknife estimators of the first-order autoregressive coefficient when the time series of interest contains a unit root. It is shown that, when the sub-samples do not overlap, the sub-sample estimators have different limiting distributions from the full-sample estimator and, hence, the jackknife estimator in its usual form does not eliminate fully the first-order bias as intended. The joint moment generating function of the numerator and denominator of these limiting distributions is derived and used to calculate the expectations that determine the optimal jackknife weights. Two methods of avoiding this procedure are proposed and investigated, one based on inclusion of an intercept in the regressions, the other based on adjusting the observations in the sub-samples. Extensions to more general augmented Dickey-Fuller (ADF) regressions are also considered. In addition to the theoretical results extensive simulations reveal the impressive bias reductions that can be obtained with these computationally simple jackknife estimators and they also highlight the importance of correct lag-length selection in ADF regressions.
1-31
Kyriacou, Maria
6234587e-81f1-4e1d-941d-395996f8bda7
Chambers, Marcus J.
6591c606-5ed7-409f-a741-77d1a13e9c39
February 2010
Kyriacou, Maria
6234587e-81f1-4e1d-941d-395996f8bda7
Chambers, Marcus J.
6591c606-5ed7-409f-a741-77d1a13e9c39
Kyriacou, Maria and Chambers, Marcus J.
(2010)
Jackknife bias reduction in the presence of a unit root
(Discussion Paper Series, 685)
Colchester, GB.
University of Essex
31pp.
Record type:
Monograph
(Discussion Paper)
Abstract
This paper analyses the properties of jackknife estimators of the first-order autoregressive coefficient when the time series of interest contains a unit root. It is shown that, when the sub-samples do not overlap, the sub-sample estimators have different limiting distributions from the full-sample estimator and, hence, the jackknife estimator in its usual form does not eliminate fully the first-order bias as intended. The joint moment generating function of the numerator and denominator of these limiting distributions is derived and used to calculate the expectations that determine the optimal jackknife weights. Two methods of avoiding this procedure are proposed and investigated, one based on inclusion of an intercept in the regressions, the other based on adjusting the observations in the sub-samples. Extensions to more general augmented Dickey-Fuller (ADF) regressions are also considered. In addition to the theoretical results extensive simulations reveal the impressive bias reductions that can be obtained with these computationally simple jackknife estimators and they also highlight the importance of correct lag-length selection in ADF regressions.
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More information
Published date: February 2010
Additional Information:
Funded by ESRC: Jackknife Methods of Estimation and Inference in Dynamic Econometric Models (RES-000-22-3082)
Identifiers
Local EPrints ID: 187103
URI: http://eprints.soton.ac.uk/id/eprint/187103
ISSN: 1755-5361
PURE UUID: 7262624a-a839-44de-a0d4-4a63523fae15
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Date deposited: 16 May 2011 13:35
Last modified: 14 Mar 2024 03:22
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Author:
Marcus J. Chambers
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