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Model averaging prediction for time series models with a diverging number of parameters

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  • Liao, Jun
  • Zou, Guohua
  • Gao, Yan
  • Zhang, Xinyu

Abstract

An important problem with the model averaging approach is the choice of weights. In this paper, a generalized Mallows model averaging (GMMA) criterion for choosing weights is developed in the context of an infinite order autoregressive (AR(∞)) process. The GMMA method adapts to the circumstances in which the dimensions of candidate models can be large and increase with the sample size. The GMMA method is shown to be asymptotically optimal in the sense of achieving the lowest out-of-sample mean squared prediction error (MSPE) for both the independent-realization and the same-realization predictions, which, as a byproduct, solves a conjecture put forward by Hansen (2008) that the well-known Mallows model averaging criterion from Hansen (2007) is asymptotically optimal for predicting the future of a time series. The rate of the GMMA-based weight estimator tending to the optimal weight vector minimizing the independent-realization MSPE is derived as well. Both simulation experiment and real data analysis illustrate the merits of the GMMA method in the prediction of an AR(∞) process.

Suggested Citation

  • Liao, Jun & Zou, Guohua & Gao, Yan & Zhang, Xinyu, 2021. "Model averaging prediction for time series models with a diverging number of parameters," Journal of Econometrics, Elsevier, vol. 223(1), pages 190-221.
    • Handle: RePEc:eee:econom:v:223:y:2021:i:1:p:190-221
    DOI: 10.1016/j.jeconom.2020.10.004
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    References listed on IDEAS

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    1. Gao, Yan & Zhang, Xinyu & Wang, Shouyang & Zou, Guohua, 2016. "Model averaging based on leave-subject-out cross-validation," Journal of Econometrics, Elsevier, vol. 192(1), pages 139-151.
    2. Ing, Ching-Kang & Wei, Ching-Zong, 2003. "On same-realization prediction in an infinite-order autoregressive process," Journal of Multivariate Analysis, Elsevier, vol. 85(1), pages 130-155, April.
    3. Michael W. McCracken & Serena Ng, 2021. "FRED-QD: A Quarterly Database for Macroeconomic Research," Review, Federal Reserve Bank of St. Louis, vol. 103(1), pages 1-44, January.
    4. Ng, Serena, 2013. "Variable Selection in Predictive Regressions," Handbook of Economic Forecasting, in: G. Elliott & C. Granger & A. Timmermann (ed.), Handbook of Economic Forecasting, edition 1, volume 2, chapter 0, pages 752-789, Elsevier.
    5. Hansen, Bruce E., 2008. "Least-squares forecast averaging," Journal of Econometrics, Elsevier, vol. 146(2), pages 342-350, October.
    6. Cheng, Xu & Hansen, Bruce E., 2015. "Forecasting with factor-augmented regression: A frequentist model averaging approach," Journal of Econometrics, Elsevier, vol. 186(2), pages 280-293.
    7. Qingfeng Liu & Ryo Okui, 2013. "Heteroscedasticity‐robust C(p) model averaging," Econometrics Journal, Royal Economic Society, vol. 16(3), pages 463-472, October.
    8. Bruce E. Hansen, 2014. "Model averaging, asymptotic risk, and regressor groups," Quantitative Economics, Econometric Society, vol. 5(3), pages 495-530, November.
    9. Xinyu Zhang & Dalei Yu & Guohua Zou & Hua Liang, 2016. "Optimal Model Averaging Estimation for Generalized Linear Models and Generalized Linear Mixed-Effects Models," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(516), pages 1775-1790, October.
    10. Liu, Chu-An, 2015. "Distribution theory of the least squares averaging estimator," Journal of Econometrics, Elsevier, vol. 186(1), pages 142-159.
    11. Tomohiro Ando & Ker-Chau Li, 2014. "A Model-Averaging Approach for High-Dimensional Regression," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(505), pages 254-265, March.
    12. 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.
    13. Ing, Ching-Kang & Sin, Chor-yiu & Yu, Shu-Hui, 2012. "Model selection for integrated autoregressive processes of infinite order," Journal of Multivariate Analysis, Elsevier, vol. 106(C), pages 57-71.
    14. 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.
    15. R. Bhansali, 1996. "Asymptotically efficient autoregressive model selection for multistep prediction," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 48(3), pages 577-602, September.
    16. Hansen, Bruce E. & Racine, Jeffrey S., 2012. "Jackknife model averaging," Journal of Econometrics, Elsevier, vol. 167(1), pages 38-46.
    17. Liang, Hua & Zou, Guohua & Wan, Alan T. K. & Zhang, Xinyu, 2011. "Optimal Weight Choice for Frequentist Model Average Estimators," Journal of the American Statistical Association, American Statistical Association, vol. 106(495), pages 1053-1066.
    18. 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.
    19. Bruce E. Hansen, 2007. "Least Squares Model Averaging," Econometrica, Econometric Society, vol. 75(4), pages 1175-1189, July.
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    Cited by:

    1. Alena Skolkova, 2023. "Model Averaging with Ridge Regularization," CERGE-EI Working Papers wp758, The Center for Economic Research and Graduate Education - Economics Institute, Prague.

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    More about this item

    Keywords

    Asymptotic optimality; Autoregressive process; Consistency; Mallows criterion; Model averaging;
    All these keywords.

    JEL classification:

    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods

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