Hostname: page-component-78c5997874-t5tsf Total loading time: 0 Render date: 2024-11-18T13:27:04.722Z Has data issue: false hasContentIssue false
  • English
  • Français

GLS-BASED UNIT ROOT TESTS WITH MULTIPLE STRUCTURAL BREAKS UNDER BOTH THE NULL AND THE ALTERNATIVE HYPOTHESES

Published online by Cambridge University Press:  01 December 2009

Josep Lluís Carrion-i-Silvestre ,
Dukpa Kim  and
Pierre Perron
Josep Lluís Carrion-i-Silvestre*
Affiliation:
University of Barcelona
Dukpa Kim
Affiliation:
University of Virginia
Pierre Perron
Affiliation:
Boston University
*
*Address correspondence to Josep Lluís Carrion-i-Silvestre, AQR Research Group, Department of Econometrics, Statistics and Spanish Economy, University of Barcelona, Av. Diagonal, 690, Barcelona, Spain 08034; e-mail: carrion@ub.edu.
Get access Rights & Permissions [Opens in a new window]

Abstract

Perron (1989, Econometrica 57, 1361–1401) introduced unit root tests valid when a break at a known date in the trend function of a time series is present. In particular, they allow a break under both the null and alternative hypotheses and are invariant to the magnitude of the shift in level and/or slope. The subsequent literature devised procedures valid in the case of an unknown break date. However, in doing so most research, in particular the commonly used test of Zivot and Andrews (1992, Journal of Business & Economic Statistics 10, 251–270), assumed that if a break occurs it does so only under the alternative hypothesis of stationarity. This is undesirable for several reasons. Kim and Perron (2009, Journal of Econometrics 148, 1–13) developed a methodology that allows a break at an unknown time under both the null and alternative hypotheses. When a break is present, the limit distribution of the test is the same as in the case of a known break date, allowing increased power while maintaining the correct size. We extend their work in several directions: (1) we allow for an arbitrary number of changes in both the level and slope of the trend function; (2) we adopt the quasi–generalized least squares detrending method advocated by Elliott, Rothenberg, and Stock (1996, Econometrica 64, 813–836) that permits tests that have local asymptotic power functions close to the local asymptotic Gaussian power envelope; (3) we consider a variety of tests, in particular the class of M-tests introduced in Stock (1999, Cointegration, Causality, and Forecasting: A Festschrift for Clive W.J. Granger) and analyzed in Ng and Perron (2001, Econometrica 69, 1519–1554).

Type
ARTICLES
Information
Econometric Theory , Volume 25 , Issue 6: Newbold Conference Special Issue , December 2009 , pp. 1754 - 1792
Copyright
Copyright © Cambridge University Press 2009

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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.CrossRefGoogle Scholar
Bai, J. (1998) A note on spurious break. Econometric Theory 14, 663–669.CrossRefGoogle Scholar
Bai, J. & Perron, P. (2003) Computation and analysis of multiple structural change models. Journal of Applied Econometrics 18, 1–22.CrossRefGoogle Scholar
Christiano, L.J. (1992) Searching for a break in GNP. Journal of Business & Economic Statistics 10, 237–250.Google Scholar
Dickey, D.A. & Fuller, W.A. (1979) Distribution of the estimators for autoregressive time series with a unit root. Journal of the American Statistical Association 74, 427–431.Google Scholar
Elliott, G., Rothenberg, T.J., & Stock, J.H. (1996) Efficient tests for an autoregressive unit root. Econometrica 64, 813–836.CrossRefGoogle Scholar
Harris, D., Harvey, D.I., Leybourne, S.J., & Taylor, A.M.R. (2009) Testing for a unit root in the presence of a possible break in trend. Econometric Theory 25, 1545–1588 (this issue).CrossRefGoogle Scholar
Harvey, D.I., Leybourne, S.J., & Newbold, P. (2001) Innovational outlier unit root tests with an endogeneously determined break in level. Oxford Bulletin of Economics and Statistics 63, 559–575.CrossRefGoogle Scholar
Hatanaka, M. & Yamada, K. (1999) A unit root test in the presence of structural changes in I(1) and I(0) models. In Engle, R.F. & White, H. (eds.), Cointegration, Causality, and Forecasting: A Festschrift in Honour of Clive W. J. Granger, pp. 256–282. Oxford University Press.CrossRefGoogle Scholar
Hecq, A. & Urbain, J.P. (1993) Misspecification tests, unit roots and level shifts. Economics Letters 43, 129–135.CrossRefGoogle Scholar
Kejriwal, M. & Perron, P. (2008) A Note on the Sequential Application of the Perron-Yabu Test for Shifts in Trend with an Integrated or Stationary Noise Component. Manuscript, Department of Economics, Boston University.Google Scholar
Kim, D. & Perron, P. (2009) Unit root tests allowing for a break in the trend function under both the null and alternative hypotheses. Journal of Econometrics 148, 1–13.CrossRefGoogle Scholar
Kim, T., Leybourne, S.J., & Newbold, P. (2000) Spurious rejections by Perron tests in the presence of a break. Oxford Bulletin of Economics and Statistics 62, 433–444.CrossRefGoogle Scholar
Lee, J. & Strazicich, M.C. (2001) Break point estimation and spurious rejections with endogenous unit root tests. Oxford Bulletin of Economics and Statistics 63, 535–558.CrossRefGoogle Scholar
Leybourne, S.J., Mills, T.C., & Newbold, P. (1998) Spurious rejections by Dickey-Fuller tests in the presence of a break under the null. Journal of Econometrics 87, 191–203.CrossRefGoogle Scholar
Leybourne, S.J. & Newbold, P. (2000) Behavior of the standard and symmetric Dickey-Fuller-type tests when there is a break under the null hypothesis. Econometrics Journal 3, 1–15.CrossRefGoogle Scholar
Montañés, A. (1997) Level shifts, unit roots and misspecification of the breaking date. Economics Letters 54, 7–13.CrossRefGoogle Scholar
Montañés, A. & Olloqui, I. (1999) Misspecification of the breaking date in segmented trend variables: Effect on the unit root tests. Economics Letters 65, 301–307.CrossRefGoogle Scholar
Ng, S. & Perron, P. (2001) Lag length selection and the construction of unit root tests with good size and power. Econometrica 69, 1519–1554.CrossRefGoogle Scholar
Nunes, L.C., Kuan, C.-M., & Newbold, P. (1995) Spurious break. Econometric Theory 11, 736–749.CrossRefGoogle Scholar
Nunes, L.C., Newbold, P., & Kuan, C.-M. (1997) Testing for unit root with breaks: Evidence on the Great Crash and the unit root hypothesis reconsidered. Oxford Bulletin of Economics and Statistics 59, 435–448.CrossRefGoogle Scholar
Perron, P. (1989) The Great Crash, the oil price shock and the unit root hypothesis. Econometrica 57, 1361–1401.CrossRefGoogle Scholar
Perron, P. (1990) Testing for a unit root in a time series with a changing mean. Journal of Business & Economic Statistics 8, 153–162.Google Scholar
Perron, P. (1997) Further evidence on breaking trend functions in macroeconomic variables. Journal of Econometrics 80, 355–385.CrossRefGoogle Scholar
Perron, P. & Ng, S. (1998) An autoregressive spectral density estimator at frequency zero for nonstationarity tests. Econometric Theory 14, 560–603.CrossRefGoogle Scholar
Perron, P. & Qu, Z. (2006) Estimating restricted structural change models. Journal of Econometrics 134, 373–399.CrossRefGoogle Scholar
Perron, P. & Qu, Z. (2007) A simple modification to improve the finite sample properties of Ng and Perron’s unit root tests. Economics Letters 94, 12–19.CrossRefGoogle Scholar
Perron, P. & Rodríguez, G.H. (2003) GLS detrending, efficient unit root tests and structural change. Journal of Econometrics 115, 1–27.CrossRefGoogle Scholar
Perron, P. & Vogelsang, T.J. (1992a) Nonstationarity and level shifts with an application to purchasing power parity. Journal of Business & Economic Statistics 10, 301–320.Google Scholar
Perron, P. & Vogelsang, T.J. (1992b) Testing for a unit root in a time series with a changing mean: Correction and extensions. Journal of Business & Economic Statistics 10, 467–470.Google Scholar
Perron, P. & Yabu, T. (2009) Testing for shifts in trend with an integrated or stationary noise component. Journal of Business and Economic Statistics 27, 369–396.CrossRefGoogle Scholar
Perron, P. & Zhu, X. (2005) Structural breaks with deterministic and stochastic trends. Journal of Econometrics 129, 65–119.CrossRefGoogle Scholar
Stock, J.H. (1999) A class of tests for integration and cointegration. In Cointegration, Causality, and Forecasting: A Festschrift for Clive W.J. Granger, pp. 135–167. Oxford University Press.CrossRefGoogle Scholar
Vogelsang, T.J. (2001) Testing for a Shift in Trend when Serial Correlation is of Unknown Form. Manuscript, Department of Economics, Cornell University.Google Scholar
Vogelsang, T.J. & Perron, P. (1998) Additional tests for a unit root allowing for a break in the trend function at an unknown time. International Economic Review 39, 1073–1100.CrossRefGoogle Scholar
Zivot, E. & Andrews, D.W.K. (1992) Further evidence on the Great Crash, the oil price shock and the unit root hypothesis. Journal of Business & Economic Statistics 10, 251–270.Google Scholar