Bootstrap, Jackknife and COLS: Bias and Mean Squared Error in Estimation of Autoregressive Models

Gareth D. Liu-Evans 1  and Garry D. A. Phillips 2
  • 1 University of Liverpool
  • 2 Cardiff University


We compare a number of bias-correction methodologies in terms of mean squared error and remaining bias, including the residual bootstrap, the relatively unexplored Quenouille jackknife, and methods based on analytical approximation of moments. We introduce a new higher-order jackknife estimator for the AR(1) with constant. Simulation results are presented for four different error structures, including GARCH. We include results for a relatively extreme situation where the errors are highly skewed and leptokurtic. It is argued that the bootstrap and analytical-correction (COLS) approaches are to be favoured overall, though the jackknife methods are the least biased. We find that COLS tends to have the lowest mean squared error, though the bootstrap also does well.

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The Journal of Time Series Econometrics (JTSE) serves as an internationally recognized outlet for important new research in both theoretical and applied classical and Bayesian time series, spatial and panel data econometrics. The scope of the journal includes papers dealing with estimation, testing and other methodological aspects involved in the application of time series and spatial analytic techniques to economic, financial and related data.