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Recursive and Sequential Tests of the Unit Root and Trend Break Hypothesis: Theory and International Evidence

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  • Anindya Banerjee
  • Robin L. Lumsdaine
  • James H. Stock

Abstract

This paper investigates the possibility, raised by Perron (1989, 1990a), that aggregate economic time series can be characterized as being stationary around broken trend lines. Unlike Perron, we treat the break date as unknown a priori. Asymptotic distributions are developed for recursive, rolling, and sequential tests for unit roots and/or changing coefficients in time series regressions. The recursive and rolling tests are based on a time series of recursively estimated coefficients, computed using increasing subsamples of the data. The sequential statistics are computed using the full data set and a sequence of regressors indexed by a "break" date. When applied to data on real postwar output from seven DECO countries, these techniques fail to reject the unit root hypothesis for five countries (including the U.S.), but suggest stationarity around a shifted trend for Japan.

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Bibliographic Info

Paper provided by National Bureau of Economic Research, Inc in its series NBER Working Papers with number 3510.

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Date of creation: Nov 1990
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Publication status: published as Journal of Business and Economic Statistics Volume 10, No. 3, pp. 271-287 July 1992
Handle: RePEc:nbr:nberwo:3510

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  1. 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, American Statistical Association, vol. 10(3), pages 251-70, July.
  2. Sargan, John Denis & Bhargava, Alok, 1983. "Testing Residuals from Least Squares Regression for Being Generated by the Gaussian Random Walk," Econometrica, Econometric Society, Econometric Society, vol. 51(1), pages 153-74, January.
  3. Perron, P., 1989. "Testing For A Unit Root In A Time Series With A Changing Mean," Papers, Princeton, Department of Economics - Econometric Research Program 347, Princeton, Department of Economics - Econometric Research Program.
  4. Donald W.K. Andrews, 1990. "Tests for Parameter Instability and Structural Change with Unknown Change Point," Cowles Foundation Discussion Papers, Cowles Foundation for Research in Economics, Yale University 943, Cowles Foundation for Research in Economics, Yale University.
  5. Mankiw, N. Gregory & Campbell, John, 1989. "International Evidence on the Persistence of Economic Fluctuations," Scholarly Articles 3224417, Harvard University Department of Economics.
  6. Sims, Christopher A & Stock, James H & Watson, Mark W, 1990. "Inference in Linear Time Series Models with Some Unit Roots," Econometrica, Econometric Society, Econometric Society, vol. 58(1), pages 113-44, January.
  7. Kramer, Walter & Ploberger, Werner & Alt, Raimund, 1988. "Testing for Structural Change in Dynamic Models," Econometrica, Econometric Society, Econometric Society, vol. 56(6), pages 1355-69, November.
  8. Cogley, T., 1989. "International Evidence On The Size Of The Random Walk In Output," Discussion Papers in Economics at the University of Washington, Department of Economics at the University of Washington 89-02, Department of Economics at the University of Washington.
  9. Nelson, Charles R. & Plosser, Charles I., 1982. "Trends and random walks in macroeconmic time series : Some evidence and implications," Journal of Monetary Economics, Elsevier, Elsevier, vol. 10(2), pages 139-162.
  10. Perron, P, 1988. "The Great Crash, The Oil Price Shock And The Unit Root Hypothesis," Papers, Princeton, Department of Economics - Econometric Research Program 338, Princeton, Department of Economics - Econometric Research Program.
  11. Harvey, A C, 1985. "Trends and Cycles in Macroeconomic Time Series," Journal of Business & Economic Statistics, American Statistical Association, American Statistical Association, vol. 3(3), pages 216-27, June.
  12. Kormendi, Roger C & Meguire, Philip, 1990. "A Multicountry Characterization of the Nonstationarity of Aggregate Output," Journal of Money, Credit and Banking, Blackwell Publishing, Blackwell Publishing, vol. 22(1), pages 77-93, February.
  13. Bhargava, Alok, 1986. "On the Theory of Testing for Unit Roots in Observed Time Series," Review of Economic Studies, Wiley Blackwell, Wiley Blackwell, vol. 53(3), pages 369-84, July.
  14. Hamilton, James D, 1989. "A New Approach to the Economic Analysis of Nonstationary Time Series and the Business Cycle," Econometrica, Econometric Society, Econometric Society, vol. 57(2), pages 357-84, March.
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