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Generalized Least Squares Model Averaging

Author

Listed:
  • Qingfeng Liu

    (Otaru University of Commerce)

  • Ryo Okui

    (Institute of Economic Research, Kyoto University)

  • Arihiro Yoshimura

    (Kyoto University)

Abstract

This paper proposes a method of averaging generalized least squares (GLS) estimators for linear regression models with heteroskedastic errors. We derive two kinds of Mallows' Cp criteria, calculated from the estimates of the mean of the squared errors of the tted value based on the averaged GLS estimators, for this class of models. The averaging weights are chosen by minimizing Mallows' Cp criterion. We show that this method achieves asymptotic optimality. It is also shown that the asymptotic optimality holds even when the variances of the error terms are estimated and the feasible generalized least squares (FGLS) estimators are averaged. Monte Carlo simulations demonstrate that averaging FGLS estimators yields an estimate that has a remarkably lower level of risk compared with averaging least squares estimators in the presence of heteroskedasticity, and it also works when heteroskedasticity is not present, in nite samples.

Suggested Citation

  • Qingfeng Liu & Ryo Okui & Arihiro Yoshimura, 2013. "Generalized Least Squares Model Averaging," KIER Working Papers 855, Kyoto University, Institute of Economic Research.
    • Handle: RePEc:kyo:wpaper:855
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    Cited by:

    1. Guozhi Hu & Weihu Cheng & Jie Zeng, 2023. "Optimal Model Averaging for Semiparametric Partially Linear Models with Censored Data," Mathematics, MDPI, vol. 11(3), pages 1-21, February.
    2. Qingfeng Liu & Qingsong Yao & Guoqing Zhao, 2020. "Model averaging estimation for conditional volatility models with an application to stock market volatility forecast," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 39(5), pages 841-863, August.
    3. Lastauskas, Povilas & Stakėnas, Julius, 2024. "Labor market policies in high- and low-interest rate environments: Evidence from the euro area," Economic Modelling, Elsevier, vol. 141(C).
    4. Mohitosh Kejriwal & Xuewen Yu, 2019. "Generalized Forecasr Averaging in Autoregressions with a Near Unit Root," Purdue University Economics Working Papers 1318, Purdue University, Department of Economics.
    5. Sun, Yuying & Hong, Yongmiao & Wang, Shouyang & Zhang, Xinyu, 2023. "Penalized time-varying model averaging," Journal of Econometrics, Elsevier, vol. 235(2), pages 1355-1377.
    6. Povilas Lastauskas & Julius Stakenas, 2019. "Does It Matter When Labor Market Reforms Are Implemented? The Role of the Monetary Policy Environment," Bank of Lithuania Working Paper Series 66, Bank of Lithuania.
    7. Cong Li & Qi Li & Jeffrey Racine & DAIQIANG ZHANG, 2017. "Optimal Model Averaging Of Varying Coefficient Models," Department of Economics Working Papers 2017-01, McMaster University.
    8. Ryan Greenaway-McGrevy & Kade Sorensen, 2021. "A spatial model averaging approach to measuring house prices," Journal of Spatial Econometrics, Springer, vol. 2(1), pages 1-32, December.
    9. Chen, Yi-Ting & Liu, Chu-An & Su, Jiun-Hua, 2025. "Bregman model averaging for forecast combination," Journal of Econometrics, Elsevier, vol. 251(C).
    10. Michael Schomaker & Christian Heumann, 2020. "When and when not to use optimal model averaging," Statistical Papers, Springer, vol. 61(5), pages 2221-2240, October.
    11. Cheng, Tzu-Chang F. & Ing, Ching-Kang & Yu, Shu-Hui, 2015. "Toward optimal model averaging in regression models with time series errors," Journal of Econometrics, Elsevier, vol. 189(2), pages 321-334.
    12. Liao, Jun & Wan, Alan T.K. & He, Shuyuan & Zou, Guohua, 2022. "Optimal model averaging for multivariate regression models," Journal of Multivariate Analysis, Elsevier, vol. 189(C).
    13. Mark F. J. Steel, 2020. "Model Averaging and Its Use in Economics," Journal of Economic Literature, American Economic Association, vol. 58(3), pages 644-719, September.
    14. Qingfeng Liu & Andrey L. Vasnev, 2019. "A Combination Method for Averaging OLS and GLS Estimators," Econometrics, MDPI, vol. 7(3), pages 1-12, September.
    15. Wenchao Xu & Xinyu Zhang, 2024. "On Asymptotic Optimality of Least Squares Model Averaging When True Model Is Included," Papers 2411.09258, arXiv.org.
    16. Yang Feng & Qingfeng Liu, 2020. "Nested Model Averaging on Solution Path for High-dimensional Linear Regression," Papers 2005.08057, arXiv.org.
    17. Longbiao Liao & Jinghao Liu, 2024. "Model Averaging for Accelerated Failure Time Models with Missing Censoring Indicators," Mathematics, MDPI, vol. 12(5), pages 1-16, February.
    18. Greenaway-McGrevy, Ryan, 2022. "Forecast combination for VARs in large N and T panels," International Journal of Forecasting, Elsevier, vol. 38(1), pages 142-164.
    19. Dong, Qingkai & Liu, Binxia & Zhao, Hui, 2023. "Weighted least squares model averaging for accelerated failure time models," Computational Statistics & Data Analysis, Elsevier, vol. 184(C).

    More about this item

    Keywords

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    JEL classification:

    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection

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