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A Rescaled Range Statistics Approach to Unit Root Tests

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  • Giuseppe Cavaliere

    (University of Bologna)

Abstract

In the framework of integrated processes, the problem of testing the presence of unknown boundaries which constrain the sample path to lie within a closed interval is considered. To discuss this inferential problem, the concept of nearly-bounded integrated process is introduced, thus allowing to define formally the concept of boundary conditions within I(1) processes. When used to detect unknown boundaries, standard unit root tests do not maintain the usual power properties and new methods need developing. Therefore a new class of tests, which are based on the rescaled range of the process, are introduced. The limiting distribution of the proposed tests can be expressed in terms of the distribution of the range of particular Brownian functionals, while the power properties are obtained through the derivation of the limiting Brownian functional of a I(1) process with boundary conditions, which is done by referring to a new invariance principles for nonstationary time series with limited sample paths. Both theoretical and simulation exercises show that range-based tests outperform standard unit root tests significantly when used to detect the presence of boundary conditions.

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Paper provided by Econometric Society in its series Econometric Society World Congress 2000 Contributed Papers with number 0318.

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Date of creation: 01 Aug 2000
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Handle: RePEc:ecm:wc2000:0318

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  1. Phillips, Peter C B & Xiao, Zhijie, 1998. " A Primer on Unit Root Testing," Journal of Economic Surveys, Wiley Blackwell, Wiley Blackwell, vol. 12(5), pages 423-69, December.
  2. Whitney K. Newey & Kenneth D. West, 1986. "A Simple, Positive Semi-Definite, Heteroskedasticity and AutocorrelationConsistent Covariance Matrix," NBER Technical Working Papers 0055, National Bureau of Economic Research, Inc.
  3. Dickey, David A & Fuller, Wayne A, 1981. "Likelihood Ratio Statistics for Autoregressive Time Series with a Unit Root," Econometrica, Econometric Society, Econometric Society, vol. 49(4), pages 1057-72, June.
  4. Mackinnon, J.G. & Haug, A.A. & Michelis, L., 1996. "Numerical Distribution Functions of Likelihood Ratio Tests for Cointegration," G.R.E.Q.A.M., Universite Aix-Marseille III 96a09, Universite Aix-Marseille III.
  5. B. Mandelbrot, 1972. "Statistical Methodology For Nonperiodic Cycles: From The Covariance To Rs Analysis," NBER Chapters, in: Annals of Economic and Social Measurement, Volume 1, number 3, pages 259-290 National Bureau of Economic Research, Inc.
  6. Dominguez, Kathryn M., 1998. "Central bank intervention and exchange rate volatility1," Journal of International Money and Finance, Elsevier, Elsevier, vol. 17(1), pages 161-190, February.
  7. Schmidt, Peter & Phillips, C B Peter, 1992. "LM Tests for a Unit Root in the Presence of Deterministic Trends," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 54(3), pages 257-87, August.
  8. Mandelbrot, Benoit B, 1971. "When Can Price Be Arbitraged Efficiently? A Limit to the Validity of the Random Walk and Martingale Models," The Review of Economics and Statistics, MIT Press, vol. 53(3), pages 225-36, August.
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Cited by:
  1. Cavaliere, Giuseppe & Xu, Fang, 2014. "Testing for unit roots in bounded time series," Journal of Econometrics, Elsevier, Elsevier, vol. 178(P2), pages 259-272.

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