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

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  • Liu-Evans Gareth D.

    (University of Liverpool)

  • Phillips Garry D. A.

    (Cardiff University)

Abstract

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.

Suggested Citation

  • Liu-Evans Gareth D. & Phillips Garry D. A., 2012. "Bootstrap, Jackknife and COLS: Bias and Mean Squared Error in Estimation of Autoregressive Models," Journal of Time Series Econometrics, De Gruyter, vol. 4(2), pages 1-35, November.
    • Handle: RePEc:bpj:jtsmet:v:4:y:2012:i:2:n:1
    DOI: 10.1515/1941-1928.1122
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    References listed on IDEAS

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    1. MacKinnon, James G. & Smith Jr., Anthony A., 1998. "Approximate bias correction in econometrics," Journal of Econometrics, Elsevier, vol. 85(2), pages 205-230, August.
    2. 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.
    3. Kiviet, Jan F. & Phillips, Garry D. A., 1996. "The bias of the ordinary least squares estimator in simultaneous equation models," Economics Letters, Elsevier, vol. 53(2), pages 161-167, November.
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    Cited by:

    1. Gareth Liu-Evans, 2021. "Improving the Estimation and Predictions of Small Time Series Models," Working Papers 202106, University of Liverpool, Department of Economics.
    2. Phillips, Garry D.A. & Liu-Evans, Gareth, 2016. "Approximating and reducing bias in 2SLS estimation of dynamic simultaneous equation models," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 734-762.
    3. Phillips, Garry David Alan & Wang, Dandan, 2019. "Bias assessment and reduction for the 2SLS estimator in general dynamic simultaneous equations models," DES - Working Papers. Statistics and Econometrics. WS 28322, Universidad Carlos III de Madrid. Departamento de Estadística.

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