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Jackknife Estimation of Stationary Autoregressive Models

  • Marcus J Chambers

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This paper reports the results of an extensive investigation into the use of the jackknife as a method of estimation in stationary autoregressive models. In addition to providing some general theoretical results concerning jackknife methods it is shown that a method based on the use of non-overlapping sub-intervals is found to work particularly well and is capable of reducing bias and root mean squared error (RMSE) compared to ordinary least squares (OLS), subject to a suitable choice of the number of sub-samples, rules-of-thumb for which are provided. The jackknife estimators also outperform OLS when the distribution of the disturbances departs from normality and when it is subject to autoregressive conditional heteroskedasticity. Furthermore the jackknife estimators are much closer to being median-unbiased than their OLS counterparts.

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File URL: http://www.essex.ac.uk/economics/discussion-papers/papers-text/dp684.pdf
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Paper provided by University of Essex, Department of Economics in its series Economics Discussion Papers with number 684.

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Date of creation: 04 Feb 2010
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Handle: RePEc:esx:essedp:684
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  1. Serena Ng & Pierre Perron, 2001. "LAG Length Selection and the Construction of Unit Root Tests with Good Size and Power," Econometrica, Econometric Society, vol. 69(6), pages 1519-1554, November.
  2. Marcus J Chambers & Maria Kyriacou, 2010. "Jackknife Bias Reduction in the Presence of a Unit Root," Economics Discussion Papers 685, University of Essex, Department of Economics.
  3. GONÇALVES, Silvia & KILIAN, Lutz, 2003. "Bootstrapping Autoregressions with Conditional Heteroskedasticity of Unknown Form," Cahiers de recherche 2003-01, Universite de Montreal, Departement de sciences economiques.
  4. Kerry Patterson, 2000. "Finite sample bias of the least squares estimator in an AR(p) model: estimation, inference, simulation and examples," Applied Economics, Taylor & Francis Journals, vol. 32(15), pages 1993-2005.
  5. Smith, Richard J., 2007. "Efficient information theoretic inference for conditional moment restrictions," Journal of Econometrics, Elsevier, vol. 138(2), pages 430-460, June.
  6. Russell Davidson & James MacKinnon, 2006. "The Case Against Jive," Departmental Working Papers 2004-02, McGill University, Department of Economics.
  7. Gospodinov, Nikolay & Otsu, Taisuke, 2012. "Local GMM estimation of time series models with conditional moment restrictions," Journal of Econometrics, Elsevier, vol. 170(2), pages 476-490.
  8. James G. MacKinnon & Russell Davidson, 2006. "Reply to Ackerberg and Devereux and Blomquist and Dahlberg on 'The case against JIVE'," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(6), pages 843-844.
  9. Tanaka, Katsuto, 1983. "Asymptotic Expansions Associated with the AR(1) Model with Unknown Mean," Econometrica, Econometric Society, vol. 51(4), pages 1221-31, July.
  10. Peter C.B. Phillips & Jun Yu, 2003. "Jackknifing Bond Option Prices," Cowles Foundation Discussion Papers 1392, Cowles Foundation for Research in Economics, Yale University.
  11. Iglesias, Emma M. & Phillips, Garry D.A., 2005. "Bivariate Arch Models: Finite-Sample Properties Of Qml Estimators And An Application To An Lm-Type Test," Econometric Theory, Cambridge University Press, vol. 21(06), pages 1058-1086, December.
  12. Andrews, Donald W K, 1993. "Exactly Median-Unbiased Estimation of First Order Autoregressive/Unit Root Models," Econometrica, Econometric Society, vol. 61(1), pages 139-65, January.
  13. Angrist, J D & Imbens, G W & Krueger, A B, 1999. "Jackknife Instrumental Variables Estimation," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 14(1), pages 57-67, Jan.-Feb..
  14. Jinyong Hahn & Whitney Newey, 2003. "Jackknife and analytical bias reduction for nonlinear panel models," CeMMAP working papers CWP17/03, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  15. Chambers, Marcus J. & Kyriacou, Maria, 2012. "Jackknife bias reduction in autoregressive models with a unit root," MPRA Paper 38255, University Library of Munich, Germany.
  16. Hahn, Jinyong & Moon, Hyungsik Roger, 2006. "Reducing Bias Of Mle In A Dynamic Panel Model," Econometric Theory, Cambridge University Press, vol. 22(03), pages 499-512, June.
  17. Yuichi Kitamura & Gautam Tripathi & Hyungtaik Ahn, 2004. "Empirical Likelihood-Based Inference in Conditional Moment Restriction Models," Econometrica, Econometric Society, vol. 72(6), pages 1667-1714, November.
  18. Jinyong Hahn & Hyungsik Roger Moon, 2005. "Reducing Bias of MLE in a Dynamic Panel Model," IEPR Working Papers 05.36, Institute of Economic Policy Research (IEPR).
  19. Kiviet, Jan F. & Phillips, Garry D.A., 1993. "Alternative Bias Approximations in Regressions with a Lagged-Dependent Variable," Econometric Theory, Cambridge University Press, vol. 9(01), pages 62-80, January.
  20. Sawa, Takamitsu, 1978. "The exact moments of the least squares estimator for the autoregressive model," Journal of Econometrics, Elsevier, vol. 8(2), pages 159-172, October.
  21. Bao, Yong, 2007. "The Approximate Moments Of The Least Squares Estimator For The Stationary Autoregressive Model Under A General Error Distribution," Econometric Theory, Cambridge University Press, vol. 23(05), pages 1013-1021, October.
  22. Bao, Yong & Ullah, Aman, 2007. "The second-order bias and mean squared error of estimators in time-series models," Journal of Econometrics, Elsevier, vol. 140(2), pages 650-669, October.
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