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Least squares estimation and tests of breaks in mean and variance under misspecification

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  • Jean-Yves Pitarakis

Abstract

In this paper we investigate the consequences of misspecification on the large sample properties of change-point estimators and the validity of tests of the null hypothesis of linearity versus the alternative of a structural break. Specifically this paper concentrates on the interaction of structural breaks in the mean and variance of a time series when either of the two is omitted from the estimation and inference procedures. Our analysis considers the case of a break in mean under omitted-regime-dependent heteroscedasticity and that of a break in variance under an omitted mean shift. The large and finite sample properties of the resulting least-squares-based estimators are investigated and the impact of the two types of misspecification on inferences about the presence or absence of a structural break subsequently analysed. Copyright Royal Economic Socciety 2004

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Article provided by Royal Economic Society in its journal The Econometrics Journal.

Volume (Year): 7 (2004)
Issue (Month): 1 (06)
Pages: 32-54

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Handle: RePEc:ect:emjrnl:v:7:y:2004:i:1:p:32-54

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  1. Terence Tai-Leung, Chong, 1997. "Structural Change in AR(1) Models," Departmental Working Papers _079, Chinese University of Hong Kong, Department of Economics.
  2. Perron, P. & Bai, J., 1995. "Estimating and Testing Linear Models with Multiple Structural Changes," Cahiers de recherche 9552, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
  3. James H. Stock & Mark W. Watson, 2003. "Has the Business Cycle Changed and Why?," NBER Chapters, in: NBER Macroeconomics Annual 2002, Volume 17, pages 159-230 National Bureau of Economic Research, Inc.
  4. James H. Stock & Mark W. Watson, 2003. "Understanding Changes in International Business Cycle Dynamics," NBER Working Papers 9859, National Bureau of Economic Research, Inc.
  5. Francis X. Diebold & Celia Chen, 1993. "Testing structural stability with endogenous break point: a size comparison of analytic and bootstrap procedures," Working Papers 93-11, Federal Reserve Bank of Philadelphia.
  6. Bruce E. Hansen, 1998. "Testing for Structural Change in Conditional Models," Boston College Working Papers in Economics 310., Boston College Department of Economics.
  7. Bai, Jushan, 1997. "Estimating Multiple Breaks One at a Time," Econometric Theory, Cambridge University Press, vol. 13(03), pages 315-352, June.
  8. M Sensier & D van Dijk, 2001. "Short-term Volatility Versus Long-term Growth: Evidence in US Macroeconomic Time Series," The School of Economics Discussion Paper Series 0103, Economics, The University of Manchester.
  9. James H. Stock & Mark W. Watson, 2003. "Has the business cycle changed?," Proceedings - Economic Policy Symposium - Jackson Hole, Federal Reserve Bank of Kansas City, pages 9-56.
  10. 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.
  11. Bruce E. Hansen, 1995. "Approximate Asymptotic P-Values for Structural Change Tests," Boston College Working Papers in Economics 297., Boston College Department of Economics.
  12. 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.
  13. Inclan, Carla, 1993. "Detection of Multiple Changes of Variance Using Posterior Odds," Journal of Business & Economic Statistics, American Statistical Association, vol. 11(3), pages 289-300, July.
  14. repec:cup:etheor:v:13:y:1997:i:3:p:315-52 is not listed on IDEAS
  15. Newey, Whitney K. & McFadden, Daniel, 1986. "Large sample estimation and hypothesis testing," Handbook of Econometrics, in: R. F. Engle & D. McFadden (ed.), Handbook of Econometrics, edition 1, volume 4, chapter 36, pages 2111-2245 Elsevier.
  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. James H. Stock & Mark W. Watson, 1998. "A Comparison of Linear and Nonlinear Univariate Models for Forecasting Macroeconomic Time Series," NBER Working Papers 6607, National Bureau of Economic Research, Inc.
  18. Andrews, Donald W K & Ploberger, Werner, 1994. "Optimal Tests When a Nuisance Parameter Is Present Only under the Alternative," Econometrica, Econometric Society, vol. 62(6), pages 1383-1414, November.
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Cited by:
  1. Konstantin A., KHOLODILIN & Wension Vincent, YAO, 2004. "Business Cycle Turning Points : Mixed-Frequency Data with Structural Breaks," Discussion Papers (IRES - Institut de Recherches Economiques et Sociales) 2004024, Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES).
  2. Oleg Glouchakov, 2006. "Joint change point estimation in regression coeffcients and variances of the errors of a linear model," Working Papers 2006_3, York University, Department of Economics.
  3. Pierre Perron & Jing Zhou, 2008. "Testing Jointly for Structural Changes in the Error Variance and Coefficients of a Linear Regression Model," Boston University - Department of Economics - Working Papers Series wp2008-011, Boston University - Department of Economics.

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