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A Combination Method for Averaging OLS and GLS Estimators

Author

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  • Qingfeng Liu

    (Department of Economics, Otaru University of Commerce, Otaru 047-8501, Japan)

  • Andrey L. Vasnev

    (Discipline of Business Analytics, The University of Sydney Business School, The University of Sydney, Sydney, NSW 2006, Australia)

Abstract

To avoid the risk of misspecification between homoscedastic and heteroscedastic models, we propose a combination method based on ordinary least-squares (OLS) and generalized least-squares (GLS) model-averaging estimators. To select optimal weights for the combination, we suggest two information criteria and propose feasible versions that work even when the variance-covariance matrix is unknown. The optimality of the method is proven under some regularity conditions. The results of a Monte Carlo simulation demonstrate that the method is adaptive in the sense that it achieves almost the same estimation accuracy as if the homoscedasticity or heteroscedasticity of the error term were known.

Suggested Citation

  • Qingfeng Liu & Andrey L. Vasnev, 2019. "A Combination Method for Averaging OLS and GLS Estimators," Econometrics, MDPI, vol. 7(3), pages 1-12, September.
    • Handle: RePEc:gam:jecnmx:v:7:y:2019:i:3:p:38-:d:265453
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    References listed on IDEAS

    as
    1. Qingfeng Liu & Ryo Okui & Arihiro Yoshimura, 2016. "Generalized Least Squares Model Averaging," Econometric Reviews, Taylor & Francis Journals, vol. 35(8-10), pages 1692-1752, December.
    2. Yuan, Zheng & Yang, Yuhong, 2005. "Combining Linear Regression Models: When and How?," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 1202-1214, December.
    3. Xie, Tian, 2017. "Heteroscedasticity-robust model screening: A useful toolkit for model averaging in big data analytics," Economics Letters, Elsevier, vol. 151(C), pages 119-122.
    4. Qingfeng Liu & Ryo Okui, 2013. "Heteroscedasticity‐robust C(p) model averaging," Econometrics Journal, Royal Economic Society, vol. 16(3), pages 463-472, October.
    5. Shangwei Zhao & Aman Ullah & Xinyu Zhang, 2018. "A Class of Model Averaging Estimators," Working Paper series 18-11, Rimini Centre for Economic Analysis.
    6. Makridakis, Spyros & Spiliotis, Evangelos & Assimakopoulos, Vassilios, 2018. "The M4 Competition: Results, findings, conclusion and way forward," International Journal of Forecasting, Elsevier, vol. 34(4), pages 802-808.
    7. Zhao, Shangwei & Ullah, Aman & Zhang, Xinyu, 2018. "A class of model averaging estimators," Economics Letters, Elsevier, vol. 162(C), pages 101-106.
    8. Zhang, Xinyu & Wan, Alan T.K. & Zou, Guohua, 2013. "Model averaging by jackknife criterion in models with dependent data," Journal of Econometrics, Elsevier, vol. 174(2), pages 82-94.
    9. Wan, Alan T.K. & Zhang, Xinyu & Zou, Guohua, 2010. "Least squares model averaging by Mallows criterion," Journal of Econometrics, Elsevier, vol. 156(2), pages 277-283, June.
    10. Hansen, Bruce E. & Racine, Jeffrey S., 2012. "Jackknife model averaging," Journal of Econometrics, Elsevier, vol. 167(1), pages 38-46.
    11. Bruce E. Hansen, 2007. "Least Squares Model Averaging," Econometrica, Econometric Society, vol. 75(4), pages 1175-1189, July.
    12. Danilov, Dmitry & Magnus, J.R.Jan R., 2004. "On the harm that ignoring pretesting can cause," Journal of Econometrics, Elsevier, vol. 122(1), pages 27-46, September.
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