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Published online by Cambridge University Press:  01 August 2009

David I. Harvey
Granger Centre for Time Series Econometrics University of Nottingham
Stephen J. Leybourne
Granger Centre for Time Series Econometrics University of Nottingham
A.M. Robert Taylor*
Granger Centre for Time Series Econometrics University of Nottingham
*Correspondence to: Robert Taylor, School of Economics, University of Nottingham, University Park, Nottingham, NG7 2RD, U.K; e-mail:


In this paper we develop a simple procedure that delivers tests for the presence of a broken trend in a univariate time series that do not require knowledge of the form of serial correlation in the data and are robust as to whether the shocks are generated by an I(0) or an I(1) process. Two trend break models are considered: the first holds the level fixed while allowing the trend to break, while the latter allows for a simultaneous break in level and trend. For the known break date case, our proposed tests are formed as a weighted average of the optimal tests appropriate for I(0) and I(1) shocks. The weighted statistics are shown to have standard normal limiting null distributions and to attain the Gaussian asymptotic local power envelope, in each case regardless of whether the shocks are I(0) or I(1). In the unknown break date case, we adopt the method of Andrews (1993) and take a weighted average of the statistics formed as the supremum over all possible break dates, subject to a trimming parameter, in both the I(0) and I(1) environments. Monte Carlo evidence suggests that our tests are in most cases more powerful, often substantially so, than the robust broken trend tests of Sayginsoy and Vogelsang (2004). An empirical application highlights the practical usefulness of our proposed tests.

Copyright © Cambridge University Press 2009

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Andrews, D.W.K. (1993) Tests for parameter instability and structural change with unknown change point. Econometrica 61, 821856.CrossRefGoogle Scholar
Andrews, D.W.K. & Ploberger, W. (1994) Optimal tests when a nuisance parameter is present only under the alternative. Econometrica 62, 13831414.CrossRefGoogle Scholar
Bai, J. & Perron, P. (1998) Estimating and testing linear models with multiple structural changes. Econometrica 66, 4778.CrossRefGoogle Scholar
Bai, J. & Perron, P. (2003) Computation and analysis of multiple structural change models. Journal of Applied Econometrics 18, 122.CrossRefGoogle Scholar
Bergstrom, A.R., Nowman, K.B., & Wymer, C.R. (1992) Gaussian estimation of a second order continuous time macroeconometric model of the UK. Economic Modelling 9, 313351.CrossRefGoogle Scholar
Breitung, J. (2002) Nonparametric tests for unit roots and cointegration. Journal of Econometrics 108, 343363.CrossRefGoogle Scholar
Hansen, B.E. (1992) Tests for parameter instability in regressions with I(1) processes. Journal of Business and Economic Statistics 10, 321335.Google Scholar
Harvey, D.I., Leybourne, S.J., & Taylor, A.M.R. (2006) Simple, robust and powerful tests of the breaking trend hypothesis. Discussion paper 06/11, University of Nottingham.Google Scholar
Jansson, M. (2002) Consistent covariance matrix estimation for linear processes. Econometric Theory 18, 14491459.CrossRefGoogle Scholar
Kwiatkowski, D., Phillips, P.C.B., Schmidt, P., & Shin, Y. (1992) Testing the null hypothesis of stationarity against the alternative of a unit root: How sure are we that economic time series have a unit root? Journal of Econometrics 54, 159178.CrossRefGoogle Scholar
Leybourne, S.J., Taylor, A.M.R., & Kim, T.-H. (2007) CUSUM of squares-based tests for a change in persistence. Journal of Time Series Analysis 28, 408433.CrossRefGoogle Scholar
Marsh, P.W.N. (2005) A measure of distance for the unit root hypothesis. Mimeo, University of York.Google Scholar
Nowman, K.B. (1998) Econometric estimation of a continuous time macroeconomic model of the United Kingdom with segmented trends. Computational Economics 12, 243254.CrossRefGoogle Scholar
Nunes, L.C., Newbold, P., & Kuan, C. (1997) Testing for unit roots with breaks: Evidence on the great crash and the unit root hypothesis reconsidered. Oxford Bulletin of Economics and Statistics 59, 435448.CrossRefGoogle Scholar
Park, J.Y. (1990) Testing for unit roots and cointegration by variable addition, in Fomby, T. and Rhodes, F. (eds.),Advances in Econometrics: Cointegration, Spurious Regression and Unit Roots. Jai Press.Google Scholar
Park, J.Y. & Choi, B. (1988) A new approach to testing for a unit root. CAE Working paper 88–23, Cornell University.Google Scholar
Perron, P. (1989) The great crash, the oil price shock, and the unit root hypothesis. Econometrica 57, 13611401.CrossRefGoogle Scholar
Perron, P. & Zhu, X. (2005) Structural breaks with deterministic and stochastic trends. Journal of Econometrics 129, 65119.CrossRefGoogle Scholar
Phillips, P.C.B. (1998) New tools for understanding spurious regressions. Econometrica 66, 12991325.CrossRefGoogle Scholar
Sayginsoy, O. & Vogelsang, T. (2004) Powerful tests of structural change that are robust to strong serial correlation. Working paper 04/08, SUNY at Albany.Google Scholar
Stock, J.H. & Watson, M.W. (1996) Evidence on structural instability in macroeconomic time series relations. Journal of Business and Economic Statistics 14, 1130.CrossRefGoogle Scholar
Stock, J.H. & Watson, M.W. (1999) A comparison of linear and nonlinear univariate models for forecasting macroeconomic time series. In Engle, R.F. and White, H. (eds.), Cointegration, Causality and Forecasting: A Festschrift in Honour of Clive W.J. Granger, 144. Oxford University Press.Google Scholar
Stock, J. & Watson, M.W., (2005) Implications of dynamic factor analysis for VAR models. NBER Working paper #11467.CrossRefGoogle Scholar
Vogelsang, T.J. (1998) Trend function hypothesis testing in the presence of serial correlation. Econometrica 66, 123148.CrossRefGoogle Scholar
Vogelsang, T.J. & Perron, P. (1998) Additional tests for a unit root allowing the possibility of breaks in the trend function. International Economic Review 39, 10731100.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 and Economic Statistics 10, 251270.CrossRefGoogle Scholar