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

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  • Boonsoo Koo

    ()

  • Myung Hwan Seo

    ()

Abstract

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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Bibliographic Info

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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Keywords: structural breaks; forecasting; mis-specification; cube-root asymptotics; bagging;

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References

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  1. Bruce E. Hansen, 1995. "Approximate Asymptotic P-Values for Structural Change Tests," Boston College Working Papers in Economics 297., Boston College Department of Economics.
  2. 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.
  3. Perron, P. & Bai, J., 1995. "Estimating and Testing Linear Models with Multiple Structural Changes," Cahiers de recherche 9552, Universite de Montreal, Departement de sciences economiques.
  4. Hwan Seo, Myung, 2011. "Estimation Of Nonlinear Error Correction Models," Econometric Theory, Cambridge University Press, vol. 27(02), pages 201-234, April.
  5. 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.
  6. 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.
  7. Donald W.K. Andrews, 1990. "Tests for Parameter Instability and Structural Change with Unknown Change Point," Cowles Foundation Discussion Papers 943, Cowles Foundation for Research in Economics, Yale University.
  8. van Dijk, Dick & Teräsvirta, Timo & Franses, Philip Hans, 2000. "Smooth Transition Autoregressive Models - A Survey of Recent Developments," Working Paper Series in Economics and Finance 380, Stockholm School of Economics, revised 17 Jan 2001.
  9. 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.
  10. Delgado, Miguel A. & Hidalgo, Javier, 2000. "Nonparametric inference on structural breaks," Journal of Econometrics, Elsevier, vol. 96(1), pages 113-144, May.
  11. 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.
  12. 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.
  13. Bruce E. Hansen, 2000. "Sample Splitting and Threshold Estimation," Econometrica, Econometric Society, vol. 68(3), pages 575-604, May.
  14. Jong, R.M. de & Davidson, J., 1996. "Consistency of Kernel Estimators of Heteroscedastic and Autocorrelated Covariance Matrices," Discussion Paper 1996-52, Tilburg University, Center for Economic Research.
  15. 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.
  16. 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.
  17. 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.
  18. 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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