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On the Long-Run Variance Ratio Test for a Unit Root

  • Ye Cai


    (Graduate Student, Department of Economics, Vanderbilt University)

  • Mototsugu Shintani


    (Department of Economics, Vanderbilt University)

This paper investigates the effects of consistent and inconsistent long-run variance estimation on a unit root test based on the generalization of the von Neumann ratio. The results from the Monte Carlo experiments suggest that the tests based on an inconsistent estimator have less size distortion and more stability of size across different autocorrelation specifications as compared to the tests based on a consistent estimator. This improvement in size property, however, comes at the cost of a loss in power. The finite sample power, as well as the local asymptotic power, of the tests with an inconsistent estimator is shown to be much lower than that of conventional tests. This finding resembles the case of the autocorrelation robust test in the standard regression context. The paper also points out that combining consistent and inconsistent estimators in the long-run variance ratio test for a unit root is one possibility of balancing the size and power.

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Paper provided by Vanderbilt University Department of Economics in its series Vanderbilt University Department of Economics Working Papers with number 0506.

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Date of creation: Mar 2005
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Handle: RePEc:van:wpaper:0506
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  1. D. Harris & D. S. Poskitt, 2004. "Determination of cointegrating rank in partially non-stationary processes via a generalised von-Neumann criterion," Econometrics Journal, Royal Economic Society, vol. 7(1), pages 191-217, 06.
  2. 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.
  3. Nabeya, Seiji & Tanaka, Katsuto, 1990. "Limiting power of unit-root tests in time-series regression," Journal of Econometrics, Elsevier, vol. 46(3), pages 247-271, December.
  4. 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.
  5. Kiefer, Nicholas M. & Bunzel, Helle & Vogelsang, Timothy & Vogelsang, Timothy & Bunzel, Helle, 2000. "Simple Robust Testing of Regression Hypotheses," Staff General Research Papers Archive 1832, Iowa State University, Department of Economics.
  6. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, vol. 59(3), pages 817-58, May.
  7. Mototsugu Shintani, 2000. "A Simple Cointegrating Rank Test Without Vector Autoregression," Vanderbilt University Department of Economics Working Papers 0044, Vanderbilt University Department of Economics.
  8. Sargan, John Denis & Bhargava, Alok, 1983. "Testing Residuals from Least Squares Regression for Being Generated by the Gaussian Random Walk," Econometrica, Econometric Society, vol. 51(1), pages 153-74, January.
  9. G. William Schwert, 1988. "Tests For Unit Roots: A Monte Carlo Investigation," NBER Technical Working Papers 0073, National Bureau of Economic Research, Inc.
  10. Peter C.B. Phillips & Joon Y. Park, 1986. "Statistical Inference in Regressions with Integrated Processes: Part 1," Cowles Foundation Discussion Papers 811R, Cowles Foundation for Research in Economics, Yale University, revised Aug 1987.
  11. Park, Joon Y. & Phillips, Peter C.B., 1989. "Statistical Inference in Regressions with Integrated Processes: Part 2," Econometric Theory, Cambridge University Press, vol. 5(01), pages 95-131, April.
  12. Phillips, Peter C B & Ouliaris, S, 1990. "Asymptotic Properties of Residual Based Tests for Cointegration," Econometrica, Econometric Society, vol. 58(1), pages 165-93, January.
  13. Kiefer, Nicholas M., 2001. "Heteroskedasticity-Autocorrelation Robust Standard Errors Using the Bartlett Kernel without Truncation," Working Papers 01-13, Cornell University, Center for Analytic Economics.
  14. 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.
  15. Peter C.B. Phillips, 1985. "Time Series Regression with a Unit Root," Cowles Foundation Discussion Papers 740R, Cowles Foundation for Research in Economics, Yale University, revised Feb 1986.
  16. Breitung, Jorg, 2002. "Nonparametric tests for unit roots and cointegration," Journal of Econometrics, Elsevier, vol. 108(2), pages 343-363, June.
  17. Michael Jansson, 2004. "The Error in Rejection Probability of Simple Autocorrelation Robust Tests," Econometrica, Econometric Society, vol. 72(3), pages 937-946, 05.
  18. Alok Bhargava, 1986. "On the Theory of Testing for Unit Roots in Observed Time Series," Review of Economic Studies, Oxford University Press, vol. 53(3), pages 369-384.
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