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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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File URL: http://www.accessecon.com/pubs/VUECON/vu05-w06.pdf
File Function: First version, 2005
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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
Contact details of provider: Web page: http://www.vanderbilt.edu/econ/wparchive/index.html

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  1. 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.
  2. Peter C.B. Phillips & Sam Ouliaris, 1987. "Asymptotic Properties of Residual Based Tests for Cointegration," Cowles Foundation Discussion Papers 847R, Cowles Foundation for Research in Economics, Yale University, revised Jul 1988.
  3. 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.
  4. 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.
  5. Kiefer, Nicholas M. & Bunzel, Helle & Vogelsang, Timothy & Vogelsang, Timothy & Bunzel, Helle, 2000. "Simple Robust Testing of Regression Hypotheses," Staff General Research Papers 1832, Iowa State University, Department of Economics.
  6. Perron, Pierre & Ng, Serena, 1996. "Useful Modifications to Some Unit Root Tests with Dependent Errors and Their Local Asymptotic Properties," Review of Economic Studies, Wiley Blackwell, vol. 63(3), pages 435-63, July.
  7. 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.
  8. Elliott, Graham & Rothenberg, Thomas J & Stock, James H, 1996. "Efficient Tests for an Autoregressive Unit Root," Econometrica, Econometric Society, vol. 64(4), pages 813-36, July.
  9. Park, Joon Y. & Phillips, Peter C.B., 1988. "Statistical Inference in Regressions with Integrated Processes: Part 1," Econometric Theory, Cambridge University Press, vol. 4(03), pages 468-497, December.
  10. Peter C.B. Phillips & Joon Y. Park, 1986. "Statistical Inference in Regressions with Integrated Processes: Part 2," Cowles Foundation Discussion Papers 819R, Cowles Foundation for Research in Economics, Yale University, revised Feb 1987.
  11. Bhargava, Alok, 1986. "On the Theory of Testing for Unit Roots in Observed Time Series," Review of Economic Studies, Wiley Blackwell, vol. 53(3), pages 369-84, July.
  12. Muller, Ulrich K., 2005. "Size and power of tests of stationarity in highly autocorrelated time series," Journal of Econometrics, Elsevier, vol. 128(2), pages 195-213, October.
  13. Peter C.B. Phillips & Pierre Perron, 1986. "Testing for a Unit Root in Time Series Regression," Cowles Foundation Discussion Papers 795R, Cowles Foundation for Research in Economics, Yale University, revised Sep 1987.
  14. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March.
  15. Mototsugu Shintani, 2000. "A Simple Cointegrating Rank Test Without Vector Autoregression," Vanderbilt University Department of Economics Working Papers 0044, Vanderbilt University Department of Economics.
  16. 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.
  17. G. William Schwert, 1988. "Tests For Unit Roots: A Monte Carlo Investigation," NBER Technical Working Papers 0073, National Bureau of Economic Research, Inc.
  18. Michael Jansson, 2004. "The Error in Rejection Probability of Simple Autocorrelation Robust Tests," Econometrica, Econometric Society, vol. 72(3), pages 937-946, 05.
  19. 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.
  20. Breitung, Jorg, 2002. "Nonparametric tests for unit roots and cointegration," Journal of Econometrics, Elsevier, vol. 108(2), pages 343-363, June.
  21. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, vol. 59(3), pages 817-58, May.
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