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Bias correction in ARMA models


  • Cordeiro, Gauss M.
  • Klein, Ruben


We give a general matrix formula for computing the bias of the exact unconditional maximum likelihood estimate in ARMA models, with known and unknown mean, up to order 1/n, where n is the length of the series. Some illustrative examples are presented.

Suggested Citation

  • Cordeiro, Gauss M. & Klein, Ruben, 1994. "Bias correction in ARMA models," Statistics & Probability Letters, Elsevier, vol. 19(3), pages 169-176, February.
  • Handle: RePEc:eee:stapro:v:19:y:1994:i:3:p:169-176

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    Cited by:

    1. Ferrari, Silvia L. P. & Cribari-Neto, Francisco, 1998. "On bootstrap and analytical bias corrections," Economics Letters, Elsevier, vol. 58(1), pages 7-15, January.
    2. Stelios Arvanitis & Antonis Demos, "undated". "A Class of Indirect Inference Estimators: Higher Order Asymptotics and Approximate Bias Correction (Revised)," DEOS Working Papers 1411, Athens University of Economics and Business, revised 23 Sep 2014.
    3. Patrick Richard, 2009. "Improving the accuracy of the analytical indirect inference estimator for MA models," Economics Bulletin, AccessEcon, vol. 29(4), pages 2795-2802.
    4. David E. Giles, 2009. "Bias Reduction for the Maximum Likelihood Estimator of the Scale Parameter in the Half-Logistic Distribution," Econometrics Working Papers 0901, Department of Economics, University of Victoria.
    5. David E. Giles & Xiao Ling, 2011. "Bias Reduction for the Maximum Likelihood Estimator of the Parameters of the Generalized Rayleigh Family of Distributions," Econometrics Working Papers 1111, Department of Economics, University of Victoria.
    6. Yong Bao, 2015. "Should We Demean the Data?," Annals of Economics and Finance, Society for AEF, vol. 16(1), pages 163-171, May.
    7. Reinsel, Gregory C. & Cheang, Wai-Kwong, 2003. "Approximate ML and REML estimation for regression models with spatial or time series AR(1) noise," Statistics & Probability Letters, Elsevier, vol. 62(2), pages 123-135, April.
    8. David E. Giles, 2012. "A Note on Improved Estimation for the Topp-Leone Distribution," Econometrics Working Papers 1203, Department of Economics, University of Victoria.
    9. Cordeiro, Gauss M. & Vasconcellos, Klaus L. P., 1997. "Bias correction for a class of multivariate nonlinear regression models," Statistics & Probability Letters, Elsevier, vol. 35(2), pages 155-164, September.
    10. Antonis Demos & Dimitra Kyriakopoulou, 2018. "Finite Sample Theory and Bias Correction of Maximum Likelihood Estimators in the EGARCH Model," DEOS Working Papers 1802, Athens University of Economics and Business.
    11. Patriota, Alexandre G. & Lemonte, Artur J., 2009. "Bias correction in a multivariate normal regression model with general parameterization," Statistics & Probability Letters, Elsevier, vol. 79(15), pages 1655-1662, August.
    12. David E. Giles & Hui Feng, 2009. "Bias of the Maximum Likelihood Estimators of the Two-Parameter Gamma Distribution Revisited," Econometrics Working Papers 0908, Department of Economics, University of Victoria.
    13. Ghitany, M.E. & Al-Mutairi, D.K. & Balakrishnan, N. & Al-Enezi, L.J., 2013. "Power Lindley distribution and associated inference," Computational Statistics & Data Analysis, Elsevier, vol. 64(C), pages 20-33.
    14. Gauss Cordeiro & Lúcia Barroso, 2007. "A third-order bias corrected estimate in generalized linear models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 16(1), pages 76-89, May.
    15. Bao, Yong & Ullah, Aman, 2007. "The second-order bias and mean squared error of estimators in time-series models," Journal of Econometrics, Elsevier, vol. 140(2), pages 650-669, October.
    16. Cordeiro, Gauss M. & Ferrari, Silvia L. P. & Uribe-Opazo, Miguel A. & Vasconcellos, Klaus L. P., 2000. "Corrected maximum-likelihood estimation in a class of symmetric nonlinear regression models," Statistics & Probability Letters, Elsevier, vol. 46(4), pages 317-328, February.
    17. F. Cribari-Neto & G.M. Cordeiro, 1995. "On Bartlett and Bartlett-Type Corrections," Econometrics 9507001, EconWPA.


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