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The Size and Power of the Bias-Corrected Bootstrap Test for Regression Models with Autocorrelated Errors

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  • Jae Kim
  • Mahbuba Yeasmin

    ()

Abstract

This paper is concerned with statistical inference for the coefficient of the linear regression model when the error term follows an autoregressive (AR) model. Past studies have reported severe size distortions, when the data are trending and autocorrelation of the error term is high. In this paper, we consider a test based on the bias-corrected bootstrap, where bias-corrected parameter estimators for the AR and regression coefficients are used. For bias-correction, the jackknife and bootstrap methods are employed. Monte Carlo simulations are conducted to compare size and power properties of the bias-corrected bootstrap test. It is found that the bias-corrected bootstrap test shows substantially improved size properties and exhibits excellent power for most of cases considered. It also appears that bootstrap bias-correction leads to better size and higher power values than jackknife bias-correction. These results are found to be robust to the choice of parameter estimation methods. Copyright Springer Science + Business Media, Inc. 2005

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File URL: http://hdl.handle.net/10.1007/s10614-005-2208-9
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Bibliographic Info

Article provided by Society for Computational Economics in its journal Computational Economics.

Volume (Year): 25 (2005)
Issue (Month): 3 (June)
Pages: 255-267

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Handle: RePEc:kap:compec:v:25:y:2005:i:3:p:255-267

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Web page: http://www.springerlink.com/link.asp?id=100248
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Keywords: bias-correction; bootstrap; jackknife; statistical inference;

References

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  1. Lutz Kilian, 1998. "Small-Sample Confidence Intervals For Impulse Response Functions," The Review of Economics and Statistics, MIT Press, vol. 80(2), pages 218-230, May.
  2. Kwok, Ben & Veall, Michael R., 1988. "The jackknife and regression with AR(1) errors," Economics Letters, Elsevier, vol. 26(3), pages 247-252.
  3. Veall, Michael R., 1986. "Bootstrapping regression estimators under first-order serial correlation," Economics Letters, Elsevier, vol. 21(1), pages 41-44.
  4. Park, Rolla Edward & Mitchell, Bridger M., 1980. "Estimating the autocorrelated error model with trended data," Journal of Econometrics, Elsevier, vol. 13(2), pages 185-201, June.
  5. Rahman, Shahidur & King, Maxwell L., 1997. "Marginal-likelihood score-based tests of regression disturbances in the presence of nuisance parameters," Journal of Econometrics, Elsevier, vol. 82(1), pages 81-106.
  6. Oxley, Leslie T & Roberts, Colin J, 1982. "Pitfalls in the Application of the Cochrane-Orcutt Technique," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 44(3), pages 227-40, August.
  7. Davidson, Russell & MacKinnon, James G., 1993. "Estimation and Inference in Econometrics," OUP Catalogue, Oxford University Press, number 9780195060119.
  8. Merton, Robert C, 1973. "An Intertemporal Capital Asset Pricing Model," Econometrica, Econometric Society, vol. 41(5), pages 867-87, September.
  9. King, M.L. & Giles, D.E.A., 1984. "Autocorrelation pre-testing in the linear model: Estimation, testing and prediction," Journal of Econometrics, Elsevier, vol. 25(1-2), pages 35-48.
  10. Rayner, Robert K., 1991. "Resampling methods for tests in regression models with autocorrelated errors," Economics Letters, Elsevier, vol. 36(3), pages 281-284, July.
  11. Rilstone, Paul, 1993. "Some improvements for bootstrapping regression estimators under first-order serial correlation," Economics Letters, Elsevier, vol. 42(4), pages 335-339.
  12. Oxley, Leslie T. & Roberts, Colin J., 1986. "Multiple minima and the Cochrane-Orcutt technique : Some initial Monte Carlo results," Economics Letters, Elsevier, vol. 20(3), pages 247-250.
  13. Maddala, G S & Rao, A S, 1973. "Tests for Serial Correlation in Regression Models with Lagged Dependent Variables and Serially Correlated Errors," Econometrica, Econometric Society, vol. 41(4), pages 761-74, July.
  14. Beach, Charles M & MacKinnon, James G, 1978. "A Maximum Likelihood Procedure for Regression with Autocorrelated Errors," Econometrica, Econometric Society, vol. 46(1), pages 51-58, January.
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