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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. Hwan Seo, Myung, 2011. "Estimation Of Nonlinear Error Correction Models," Econometric Theory, Cambridge University Press, vol. 27(02), pages 201-234, April.
  2. Dick van Dijk & Timo Terasvirta & Philip Hans Franses, 2002. "Smooth Transition Autoregressive Models — A Survey Of Recent Developments," Econometric Reviews, Taylor & Francis Journals, vol. 21(1), pages 1-47.
  3. Hansen, Bruce E, 1997. "Approximate Asymptotic P Values for Structural-Change Tests," Journal of Business & Economic Statistics, American Statistical Association, vol. 15(1), pages 60-67, January.
  4. Bruce E. Hansen, 2000. "Sample Splitting and Threshold Estimation," Econometrica, Econometric Society, vol. 68(3), pages 575-604, May.
  5. Bruce E. Hansen, 2001. "The New Econometrics of Structural Change: Dating Breaks in U.S. Labour Productivity," Journal of Economic Perspectives, American Economic Association, vol. 15(4), pages 117-128, Fall.
  6. 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.
  7. Jushan Bai & Pierre Perron, 1998. "Estimating and Testing Linear Models with Multiple Structural Changes," Econometrica, Econometric Society, vol. 66(1), pages 47-78, January.
  8. 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.
  9. Pesaran, M. Hashem & Timmermann, Allan, 2007. "Selection of estimation window in the presence of breaks," Journal of Econometrics, Elsevier, vol. 137(1), pages 134-161, March.
  10. Andrews, Donald W K, 1993. "Tests for Parameter Instability and Structural Change with Unknown Change Point," Econometrica, Econometric Society, vol. 61(4), pages 821-56, July.
  11. Heather M. Anderson & George Athanasopoulos & Farshid Vahid, 2002. "Nonlinear Autoregresssive Leading Indicator Models of Output in G-7 Countries," Monash Econometrics and Business Statistics Working Papers 20/02, Monash University, Department of Econometrics and Business Statistics.
  12. 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.
  13. Andrews, Donald W.K., 1988. "Laws of Large Numbers for Dependent Non-Identically Distributed Random Variables," Econometric Theory, Cambridge University Press, vol. 4(03), pages 458-467, December.
  14. James H. Stock & Mark W. Watson, 1994. "Evidence on structural instability in macroeconomic times series relations," Working Paper Series, Macroeconomic Issues 94-13, Federal Reserve Bank of Chicago.
  15. Dan Ben-David & David H. Papell, 1997. "Slowdowns and Meltdowns: Postwar Growth Evidence from 74 Countries," NBER Working Papers 6266, National Bureau of Economic Research, Inc.
  16. Jushan Bai, 1997. "Estimation Of A Change Point In Multiple Regression Models," The Review of Economics and Statistics, MIT Press, vol. 79(4), pages 551-563, November.
  17. Tian, Jing & Anderson, Heather M., 2014. "Forecast combinations under structural break uncertainty," International Journal of Forecasting, Elsevier, vol. 30(1), pages 161-175.
  18. Robert M. De Jong & James Davidson, 2000. "Consistency of Kernel Estimators of Heteroscedastic and Autocorrelated Covariance Matrices," Econometrica, Econometric Society, vol. 68(2), pages 407-424, March.
  19. 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.
  20. Delgado, Miguel A. & Hidalgo, Javier, 2000. "Nonparametric inference on structural breaks," Journal of Econometrics, Elsevier, vol. 96(1), pages 113-144, May.
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