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Estimating Multiple Breaks One at a Time

Published online by Cambridge University Press:  11 February 2009

Jushan Bai
Jushan Bai
Affiliation:
Massachusetts Institute of Technology
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Abstract

Sequential (one-by-one) rather than simultaneous estimation of multiple breaks is investigated in this paper. The advantage of this method lies in its computational savings and its robustness to misspecification in the number of breaks. The number of least-squares regressions required to compute all of the break points is of order T, the sample size. Each estimated break point is shown to be consistent for one of the true ones despite underspecification of the number of breaks. More interestingly and somewhat surprisingly, the estimated break points are shown to be T-consistent, the same rate as the simultaneous estimation. Limiting distributions are also derived. Unlike simultaneous estimation, the limiting distributions are generally not symmetric and are influenced by regression parameters of all regimes. A simple method is introduced to obtain break point estimators that have the same limiting distributions as those obtained via simultaneous estimation. Finally, a procedure is proposed to consistently estimate the number of breaks.

Type
Articles
Information
Econometric Theory , Volume 13 , Issue 3 , June 1997 , pp. 315 - 352
Copyright
Copyright © Cambridge University Press 1997

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References

REFERENCES

Andrews, D.W.K. & Ploberger, W. (1994) Optimal tests when a nuisance parameter is present only under the alternative. Econometrica 62, 1383–1414.Google Scholar
Bai, J. (1994a) Estimation of Structural Change based on Wald Type Statistics. Working paper 94-6, Department of Economics, MIT, Cambridge, Massachusetts (forthcoming in Review of Economics and Statistics).Google Scholar
Bai, J. (1994b) Least squares estimation of a shift in linear processes. Journal of Time Series Analysis 15, 453–472.CrossRefGoogle Scholar
Bai, J. & Perron, P. (1994) Testing for and Estimation of Multiple Structural Changes! Manuscript, Department of Economics, MIT, Cambridge, Massachusetts.Google Scholar
Burdekin, R.C.K. & Siklos, CM. (1995) Exchange Rate Regimes and Inflation Persistence: Further Evidence. Manuscript, Department of Economics, University of California at San Diego.Google Scholar
Chong, T.T.-L. (1994) Consistency of Change-Point Estimators When the Number of Change-Points in Structural Change Models Is Underspecified. Manuscript, Department of Economics, University of Rochester, Rochester, New York.Google Scholar
Cooper, S.J. (1995) Multiple Regimes in U.S. Output Fluctuations. Manuscript, Kennedy School of Government, Harvard University, Cambridge, Massachusetts.Google Scholar
DeLong, D.M. (1981) Crossing probabilities for a square root boundary by a Bessel process. Communications in Statistics-Theory and Methods, A 10 (21), 2197–2213.CrossRefGoogle Scholar
Garcia, R. & Perron, P. (1996) An analysis of the real interest rate under regime shifts. Review of Economics and Statistics 78, 111–125.CrossRefGoogle Scholar
Lumsdaine, R.L. and Papell, D.H. (1995) Multiple Trend Breaks and the Unit Root Hypothesis. Manuscript, Princeton University.Google Scholar
Phillips, P.C.B. & Solo, V. (1992) Asymptotics for linear processes. Annals of Statistics 20, 971–1001.Google Scholar
Yao, Y.-C. (1988) Estimating the number of change-points via Schwarz' criterion. Statistics and Probability Letters 6, 181–189.CrossRefGoogle Scholar