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Structural-break models under mis-specification: implications for forecasting

  • Boonsoo Koo

    ()

  • Myung Hwan Seo

    ()

This paper revisits the least squares estimator of the linear regression with a structural break. We view the model as an approximation to the true data generating process whose exact nature is unknown but perhaps changing over time either continuously or with some jumps. This view is widely held in the forecasting literature and under this view, the time series dependence property of all the observed variables is unstable as well. We establish that the rate of convergence of the estimator to a properly defined limit is much slower than the standard super consistent rate, even slower than the square root of the sample size T and as slow as the cube root of T. We also provide an asymptotic distribution of the estimator and that of the Gaussian quasi likelihood ratio statistic for a certain class of true data generating process. We relate our finding to current forecast combination methods and bagging and propose a new averaging scheme. The performance of various contemporary forecasting methods is compared to ours using a number of macroeconomic data.

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File URL: http://www.buseco.monash.edu.au/ebs/pubs/wpapers/2013/wp11-13.pdf
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Paper provided by Monash University, Department of Econometrics and Business Statistics in its series Monash Econometrics and Business Statistics Working Papers with number 11/13.

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Date of creation: 2013
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Handle: RePEc:msh:ebswps:2013-11
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  1. van Dijk, D.J.C. & Terasvirta, T. & Franses, Ph.H.B.F., 2000. "Smooth transition autoregressive models - A survey of recent developments," Econometric Institute Research Papers EI 2000-23/A, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
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  11. Ben-David, Dan & Papell, David, 1995. "Slowdowns and Meltdowns: Post-war Growth Evidence from 74 Countries," CEPR Discussion Papers 1111, C.E.P.R. Discussion Papers.
  12. Delgado, Miguel A. & Hidalgo, Javier, 2000. "Nonparametric inference on structural breaks," Journal of Econometrics, Elsevier, vol. 96(1), pages 113-144, May.
  13. Pesaran, M. Hashem & Pick, Andreas, 2011. "Forecast Combination Across Estimation Windows," Journal of Business & Economic Statistics, American Statistical Association, vol. 29(2), pages 307-318.
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  15. Wooldridge, Jeffrey M. & White, Halbert, 1988. "Some Invariance Principles and Central Limit Theorems for Dependent Heterogeneous Processes," Econometric Theory, Cambridge University Press, vol. 4(02), pages 210-230, August.
  16. Bruce E. Hansen, 1996. "Sample Splitting and Threshold Estimation," Boston College Working Papers in Economics 319., Boston College Department of Economics, revised 12 May 1998.
  17. Pesaran, M. Hashem & Pick, Andreas & Pranovich, Mikhail, 2013. "Optimal forecasts in the presence of structural breaks," Journal of Econometrics, Elsevier, vol. 177(2), pages 134-152.
  18. Hansen, Bruce E., 2009. "Averaging Estimators For Regressions With A Possible Structural Break," Econometric Theory, Cambridge University Press, vol. 25(06), pages 1498-1514, December.
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  20. Tian, Jing & Anderson, Heather M., 2014. "Forecast combinations under structural break uncertainty," International Journal of Forecasting, Elsevier, vol. 30(1), pages 161-175.
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