Jackknife Bias Reduction in the Presence of a Unit Root
AbstractThis 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 InfoPaper provided by University of Essex, Department of Economics in its series Economics Discussion Papers with number 685.
Date of creation: 04 Feb 2010
Date of revision:
Postal: Discussion Papers Administrator, Department of Economics, University of Essex, Wivenhoe Park, Colchester CO4 3SQ, U.K.
This paper has been announced in the following NEP Reports:
- NEP-ALL-2010-03-06 (All new papers)
- NEP-ECM-2010-03-06 (Econometrics)
- NEP-ETS-2010-03-06 (Econometric Time Series)
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