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Jackknife Bias Reduction in the Presence of a Unit Root

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  • Marcus J Chambers

    ()

  • Maria Kyriacou

    ()

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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Bibliographic Info

Paper provided by University of Essex, Department of Economics in its series Economics Discussion Papers with number 685.

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Date of creation: 04 Feb 2010
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Handle: RePEc:esx:essedp:685

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  1. Serena Ng & Pierre Perron, 1997. "Lag Length Selection and the Construction of Unit Root Tests with Good Size and Power," Boston College Working Papers in Economics 369, Boston College Department of Economics, revised 01 Sep 2000.
  2. Jinyong Hahn & Whitney Newey, 2004. "Jackknife and Analytical Bias Reduction for Nonlinear Panel Models," Econometrica, Econometric Society, vol. 72(4), pages 1295-1319, 07.
  3. Niels Haldrup & Michael Jansson, 2005. "Improving Size and Power in Unit Root Testing," Economics Working Papers 2005-2, School of Economics and Management, University of Aarhus.
  4. Peter C.B. Phillips, 1985. "Time Series Regression with a Unit Root," Cowles Foundation Discussion Papers 740R, Cowles Foundation for Research in Economics, Yale University, revised Feb 1986.
  5. Gonzalo, Jesús & Pitarakis, Jean-Yves, . "On the exact moments of asymptotic distributions in an unstable Ar(1) with dependent errors," Open Access publications from Universidad Carlos III de Madrid info:hdl:10016/752, Universidad Carlos III de Madrid.
  6. DHAENE, Geert & JOCHMANS, Koen, 2010. "Split-panel jackknife estimation of fixed-effect models," CORE Discussion Papers 2010003, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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Cited by:
  1. Ye Chen & Jun Yu, 2011. "Optimal Jackknife for Discrete Time and Continuous Time Unit Root Models," Working Papers 12-2011, Singapore Management University, School of Economics.
  2. Chambers, Marcus J., 2013. "Jackknife estimation of stationary autoregressive models," Journal of Econometrics, Elsevier, vol. 172(1), pages 142-157.
  3. Kyriacou, Maria, 2012. "Overlapping sub-sampling and invariance to initial conditions," Discussion Paper Series In Economics And Econometrics 1203, Economics Division, School of Social Sciences, University of Southampton.

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