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Averaging Estimators For Regressions With A Possible Structural Break

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  • Hansen, Bruce E.

Abstract

This paper investigates selection and averaging of linear regressions with a possible structural break. Our main contribution is the construction of a Mallows criterion for the structural break model. We show that the correct penalty term is nonstandard and depends on unknown parameters, but it can be approximated by an average of limiting cases to yield a feasible penalty with good performance. Following Hansen (2007, Econometrica 75, 1175–1189) we recommend averaging the structural break estimates with the no-break estimates where the weight is selected to minimize the Mallows criterion. This estimator is simple to compute, as the weights are a simple function of the ratio of the penalty to the Andrews SupF test statistic.To assess performance we focus on asymptotic mean-squared error (AMSE) in a local asymptotic framework. We show that the AMSE of the estimators depends exclusively on the parameter variation function. Numerical comparisons show that the unrestricted least-squares and pretest estimators have very large AMSE for certain regions of the parameter space, whereas our averaging estimator has AMSE close to the infeasible optimum.

Suggested Citation

  • Hansen, Bruce E., 2009. "Averaging Estimators For Regressions With A Possible Structural Break," Econometric Theory, Cambridge University Press, vol. 25(6), pages 1498-1514, December.
    • Handle: RePEc:cup:etheor:v:25:y:2009:i:06:p:1498-1514_99
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    Cited by:

    1. Yin, Anwen, 2015. "Forecasting and model averaging with structural breaks," ISU General Staff Papers 201501010800005727, Iowa State University, Department of Economics.
    2. Hansen, Bruce E., 2010. "Averaging estimators for autoregressions with a near unit root," Journal of Econometrics, Elsevier, vol. 158(1), pages 142-155, September.
    3. Gallegati, Marco & Ramsey, James B., 2013. "Structural change and phase variation: A re-examination of the q-model using wavelet exploratory analysis," Structural Change and Economic Dynamics, Elsevier, vol. 25(C), pages 60-73.
    4. 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.
    5. Tom Boot & Andreas Pick, 2017. "A near optimal test for structural breaks when forecasting under square error loss," Tinbergen Institute Discussion Papers 17-039/III, Tinbergen Institute.
    6. Liu, Chu-An, 2012. "A plug-in averaging estimator for regressions with heteroskedastic errors," MPRA Paper 41414, University Library of Munich, Germany.
    7. Yan Gao & Xinyu Zhang & Shouyang Wang & Terence Tai-leung Chong & Guohua Zou, 2019. "Frequentist model averaging for threshold models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 71(2), pages 275-306, April.
    8. Koo, Bonsoo & Seo, Myung Hwan, 2015. "Structural-break models under mis-specification: Implications for forecasting," Journal of Econometrics, Elsevier, vol. 188(1), pages 166-181.
    9. Kurozumi, Eiji & Tuvaandorj, Purevdorj, 2011. "Model selection criteria in multivariate models with multiple structural changes," Journal of Econometrics, Elsevier, vol. 164(2), pages 218-238, October.
    10. Zhao, Shangwei & Xie, Tian & Ai, Xin & Yang, Guangren & Zhang, Xinyu, 2023. "Correcting sample selection bias with model averaging for consumer demand forecasting," Economic Modelling, Elsevier, vol. 123(C).
    11. Ahmed, Osama, 2021. "Do future markets protect the spot markets in developing countries? The case of the Egyptian wheat market," EconStor Open Access Articles and Book Chapters, ZBW - Leibniz Information Centre for Economics, vol. 20(5), pages 65-83.
    12. Anwen Yin, 2019. "Equity Premium Prediction with Structural Breaks: A Two-Stage Forecast Combination Approach," International Journal of Economics and Finance, Canadian Center of Science and Education, vol. 11(12), pages 1-50, December.
    13. Liu, Chu-An, 2015. "Distribution theory of the least squares averaging estimator," Journal of Econometrics, Elsevier, vol. 186(1), pages 142-159.
    14. Elena Andreou & Eric Ghysels & Constantinos Kourouyiannis, 2012. "Robust volatility forecasts in the presence of structural breaks," University of Cyprus Working Papers in Economics 08-2012, University of Cyprus Department of Economics.
    15. Lu, Xun & Su, Liangjun, 2015. "Jackknife model averaging for quantile regressions," Journal of Econometrics, Elsevier, vol. 188(1), pages 40-58.
    16. Tae‐Hwy Lee & Shahnaz Parsaeian & Aman Ullah, 2022. "Optimal forecast under structural breaks," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 37(5), pages 965-987, August.
    17. Anwen Yin, 2024. "Predictive model averaging with parameter instability and heteroskedasticity," Bulletin of Economic Research, Wiley Blackwell, vol. 76(2), pages 418-442, April.
    18. Shahnaz Parsaeian, 2024. "Stein-like Common Correlated Effects Estimation under Structural Breaks," Econometrics, MDPI, vol. 12(2), pages 1-23, April.
    19. Boot, Tom & Pick, Andreas, 2020. "Does modeling a structural break improve forecast accuracy?," Journal of Econometrics, Elsevier, vol. 215(1), pages 35-59.
    20. Tian Xie, 2019. "Forecast Bitcoin Volatility with Least Squares Model Averaging," Econometrics, MDPI, vol. 7(3), pages 1-20, September.
    21. Chu-An Liu & Biing-Shen Kuo & Wen-Jen Tsay, 2017. "Autoregressive Spectral Averaging Estimator," IEAS Working Paper : academic research 17-A013, Institute of Economics, Academia Sinica, Taipei, Taiwan.

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