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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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Author Info

  • Fabio Busetti
  • Andrew C Harvey

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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Bibliographic Info

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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Web page: http://sticerd.lse.ac.uk/_new/publications/default.asp

Related research

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

References

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  1. Kwiatkowski, D. & Phillips, P.C.B. & Schmidt, P., 1990. "Testing the Null Hypothesis of Stationarity Against the Alternative of Unit Root : How Sure are we that Economic Time Series have a Unit Root?," Papers, Michigan State - Econometrics and Economic Theory 8905, Michigan State - Econometrics and Economic Theory.
  2. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, Econometric Society, vol. 59(3), pages 817-58, May.
  3. Nyblom, Jukka & Harvey, Andrew, 2000. "Tests Of Common Stochastic Trends," Econometric Theory, Cambridge University Press, vol. 16(02), pages 176-199, April.
  4. Hao, K., 1996. "Testing for Structural Change in Cointegrated Regression Models: Some Comparisons and Generalizations," Monash Econometrics and Business Statistics Working Papers, Monash University, Department of Econometrics and Business Statistics 3/96, Monash University, Department of Econometrics and Business Statistics.
  5. Leybourne, S J & McCabe, B P M, 1994. "A Consistent Test for a Unit Root," Journal of Business & Economic Statistics, American Statistical Association, American Statistical Association, vol. 12(2), pages 157-66, April.
  6. Eric Zivot & Donald W.K. Andrews, 1990. "Further Evidence on the Great Crash, the Oil Price Shock, and the Unit Root Hypothesis," Cowles Foundation Discussion Papers 944, Cowles Foundation for Research in Economics, Yale University.
  7. 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, American Statistical Association, vol. 13(3), pages 237-52, July.
  8. 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.
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Citations

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Cited by:
  1. Tommaso Proietti & Alberto Musso & Thomas Westermann, 2007. "Estimating potential output and the output gap for the euro area: a model-based production function approach," Empirical Economics, Springer, Springer, vol. 33(1), pages 85-113, July.
  2. Anton Skrobotov, 2012. "Bias Correction of KPSS Test with Structural Break for Reducing of Size Distortion," Working Papers 0043, Gaidar Institute for Economic Policy, revised 2013.
  3. Cavaliere, Giuseppe & Taylor, A.M. Robert, 2008. "Testing for a change in persistence in the presence of non-stationary volatility," Journal of Econometrics, Elsevier, Elsevier, vol. 147(1), pages 84-98, November.
  4. Proietti, Tommaso & Musso, Alberto, 2007. "Growth accounting for the euro area: a structural approach," Working Paper Series 0804, European Central Bank.
  5. Westerlund, Joakim & Edgerton , David, 2006. "New Improved Tests for Cointegration with Structural Breaks," Working Papers 2006:3, Lund University, Department of Economics.
  6. Josep Llu�s Carrion-i-Silvestre & Tom�s del Barrio-Castro & Enrique L�pez-Bazo, 2005. "Breaking the panels: An application to the GDP per capita," Econometrics Journal, Royal Economic Society, vol. 8(2), pages 159-175, 07.
  7. Landajo, Manuel & Presno, María José, 2010. "Nonparametric pseudo-Lagrange multiplier stationarity testing," MPRA Paper 25659, University Library of Munich, Germany.
  8. 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.
  9. María Presno & Manuel Landajo, 2010. "Computation of limiting distributions in stationarity testing with a generic trend," Metrika, Springer, Springer, vol. 71(2), pages 165-183, March.
  10. Kaddour Hadri & Yao Rao, 2008. "Panel Stationarity Test with Structural Breaks," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 70(2), pages 245-269, 04.
  11. Andre Jungmittag & Hariolf Grupp, 2006. "Wechselwirkungen zwischen Innovations- und Wachstumsprozessen in Deutschland 1951-1999 im Vergleich zu 1850-1913," Journal of Economics and Statistics (Jahrbuecher fuer Nationaloekonomie und Statistik), Justus-Liebig University Giessen, Department of Statistics and Economics, Justus-Liebig University Giessen, Department of Statistics and Economics, vol. 226(2), pages 180-207, March.

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