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Testing for the Presence of a Random Walk in Series with Structural Breaks - (Now published in Journal of Time Series Analysis, 22 (2001), pp.127-150.)

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Fabio Busetti
Andrew C Harvey

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Abstract

The paper considers tests for the presence of a random walk component in a stationary or trend stationary time series and extends them to series which contain structural breaks. The locally best invariant (LBI) test is derived and the asymptotic distribution obtained. Then a modified test statistic is proposed. The advantage of this statistic is that its asymptotic distribution is not dependent on the location of the breakpoint and its form is that of the generalised Cram?r-von Mises distribution, with degrees of freedom depending on the number of breakpoints. The performance of this modified test is shown, via some simulation experiments, to be comparable to that of the LBI test. An unconditional test, based on the assymption that there is a single break at an unknown point is also examined. The use of the tests is illustrated with data on the flow of the Nile and US Gross National Product.

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Paper provided by Suntory and Toyota International Centres for Economics and Related Disciplines, LSE in its series STICERD - Econometrics Paper Series with number /1998/365.

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Date of creation: Dec 1998
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Handle: RePEc:cep:stiecm:/1998/365

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Related research
Keywords: Brownian bridge; Cram?r-von Mises distribution; intervention analysis; locally best invariant test; structural time series model; unobserved components.;

References listed on IDEAS
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  1. 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. [Downloadable!] (restricted)
  2. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, vol. 59(3), pages 817-58, May. [Downloadable!] (restricted)
    Other versions:
  3. Nyblom, Jukka & Harvey, Andrew, 1999. "Tests of Common Stochastic Trends," Cambridge Working Papers in Economics 9902, Faculty of Economics, University of Cambridge.
    Other versions:
  4. Zivot, Eric & Andrews, Donald W K, 1992. "Further Evidence on the Great Crash, the Oil-Price Shock, and the Unit-Root Hypothesis," Journal of Business & Economic Statistics, American Statistical Association, vol. 10(3), pages 251-70, July.
    Other versions:
  5. Hao, K., 1996. "Testing for Structural Change in Cointegrated Regression Models: Some Comparisons and Generalizations," Monash Econometrics and Business Statistics Working Papers 3/96, Monash University, Department of Econometrics and Business Statistics.
  6. Canova, Fabio & Hansen, Bruce E, 1995. "Are Seasonal Patterns Constant over Time? A Test for Seasonal Stability," Journal of Business & Economic Statistics, American Statistical Association, vol. 13(3), pages 237-52, July.
  7. Kang Hao, 1996. "Testing for structural change in cointegrated regression models: some comparisons and generalizations," Econometric Reviews, Taylor and Francis Journals, vol. 15(4), pages 401-429. [Downloadable!] (restricted)
  8. Leybourne, S J & McCabe, B P M, 1994. "A Consistent Test for a Unit Root," Journal of Business & Economic Statistics, American Statistical Association, vol. 12(2), pages 157-66, April.
  9. Kwiatkowski, Denis & Phillips, Peter C. B. & Schmidt, Peter & Shin, Yongcheol, 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, Elsevier, vol. 54(1-3), pages 159-178. [Downloadable!] (restricted)
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Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Jushan Bai; Josep Lluís Carrion-i-Silvestre, 2004. "Structural changes, common stochastic trends and unit roots in panel data," Econometric Society 2004 North American Summer Meetings 345, Econometric Society. [Downloadable!]
    Other versions:
  2. Tommaso PROIETTI & Alberto MUSSO & Thomas WESTERMANN, 2002. "Estimating Potential Output and the Output Gap for the Euro Area: a Model-Based Production Function Approach," Economics Working Papers ECO2002/09, European University Institute. [Downloadable!]
    Other versions:
  3. Josep Lluis Carrion Silvestre & Tomas del Barrio Castro & Enrique Lopez Bazo, 2003. "Breaking the panels. An application to the GDP per capita," Working Papers in Economics 97, Universitat de Barcelona. Espai de Recerca en Economia. [Downloadable!]
    Other versions:
  4. Tommaso Proietti & Alberto Musso, 2007. "Growth accounting for the Euro area - a structural approach," Working Paper Series 804, European Central Bank. [Downloadable!]
  5. Yoichi Arai & Eiji Kurozumi, 2005. "Testing for the Null Hypothesis of Cointegration with Structural Breaks," CIRJE F-Series CIRJE-F-319, CIRJE, Faculty of Economics, University of Tokyo. [Downloadable!]
  6. Westerlund, Joakim & Edgerton , David, 2006. "New Improved Tests for Cointegration with Structural Breaks," Working Papers 2006:3, Lund University, Department of Economics.
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