A Rescaled Range Statistics Approach to Unit Root Tests
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.
|Date of creation:||01 Aug 2000|
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- 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.
- Newey, Whitney & West, Kenneth, 2014. "A simple, positive semi-definite, heteroscedasticity and autocorrelation consistent covariance matrix," Applied Econometrics, Publishing House "SINERGIA PRESS", vol. 33(1), pages 125-132.
- Newey, Whitney K & West, Kenneth D, 1987. "A Simple, Positive Semi-definite, Heteroskedasticity and Autocorrelation Consistent Covariance Matrix," Econometrica, Econometric Society, vol. 55(3), pages 703-08, May.
- Peter C.B. Phillips & Zhijie Xiao, 1998.
"A Primer on Unit Root Testing,"
Cowles Foundation Discussion Papers
1189, Cowles Foundation for Research in Economics, Yale University.
- Peter C. B. Phillips & Zhijie Xiao, 1998. "A Primer on Unit Root Testing," Journal of Economic Surveys, Wiley Blackwell, vol. 12(5), pages 423-470, December.
- Phillips, Peter C B & Xiao, Zhijie, 1998. " A Primer on Unit Root Testing," Journal of Economic Surveys, Wiley Blackwell, vol. 12(5), pages 423-69, December.
- 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.
- MacKinnon, James G & Haug, Alfred A & Michelis, Leo, 1999.
"Numerical Distribution Functions of Likelihood Ratio Tests for Cointegration,"
Journal of Applied Econometrics,
John Wiley & Sons, Ltd., vol. 14(5), pages 563-77, Sept.-Oct.
- Mackinnon, J.G. & Haug, A.A. & Michelis, L., 1996. "Numerical Distribution Functions of Likelihood Ratio Tests for Cointegration," G.R.E.Q.A.M. 96a09, Universite Aix-Marseille III.
- James G. MacKinnon & Alfred A. Haug & Leo Michelis, 1996. "Numerical Distribution Functions of Likelihood Ratio Tests for Cointegration," Working Papers 1996_07, York University, Department of Economics.
- Dickey, David A & Fuller, Wayne A, 1981. "Likelihood Ratio Statistics for Autoregressive Time Series with a Unit Root," Econometrica, Econometric Society, vol. 49(4), pages 1057-72, June.
- 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.
- Dominguez, Kathryn M., 1998. "Central bank intervention and exchange rate volatility1," Journal of International Money and Finance, Elsevier, vol. 17(1), pages 161-190, February.
- B. Mandelbrot, 1972. "Statistical Methodology for Nonperiodic Cycles: From the Covariance To R/S Analysis," NBER Chapters, in: Annals of Economic and Social Measurement, Volume 1, number 3, pages 259-290 National Bureau of Economic Research, Inc.
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