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Bootstrapping Unit Root Tests with Covariates

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  • Chang, Yoosoon

    (Rice U)

  • Sickles, Robin
  • Song, Wonho

Abstract

We consider the bootstrap method for the covariates augmented Dickey-Fuller (CADF) unit root test suggested in Hansen (1995) which uses related variables to improve the power of univariate unit root tests. It is shown that there are substantial power gains from including correlated covariates. The limit distribution of the CADF test, however, depends on the nuisance parameter that represents the correlation between the equation error and the covariates. Hence, inference based directly on the CADF test is not possible. To provide a valid inferential basis for the CADF test, we propose to use the bootstrap procedure to obtain critical values, and establish the asymptotic validity of the bootstrap CADF test. Simulations show that the bootstrap CADF test significantly improves the finite sample size performances of the CADF test, especially when the covariates are highly correlated with the error. Indeed, the bootstrap CADF test offers drastic power gains over the conventional ADF test. We apply our testing procedures to the extended Nelson-Plosser data set for the post-1929 samples as well as postwar annual CPI-based real exchange rates for 14 OECD countries.

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Bibliographic Info

Paper provided by Rice University, Department of Economics in its series Working Papers with number 2001-07.

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Date of creation: Sep 2001
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Handle: RePEc:ecl:riceco:2001-07

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  1. Jeffrey A. Frankel and Andrew K. Rose., 1995. "A Panel Project on Purchasing Power Parity: Mean Reversion Within and Between Countries," Center for International and Development Economics Research (CIDER) Working Papers C95-052, University of California at Berkeley.
  2. Alston Flynn, N. & Boucher, Janice L., 1993. "Tests of long-run Purchasing Power Parity using alternative methodologies," Journal of Macroeconomics, Elsevier, vol. 15(1), pages 109-122.
  3. repec:att:wimass:9716 is not listed on IDEAS
  4. DeJong, David N. & Nankervis, John C. & Savin, N. E. & Whiteman, Charles H., 1992. "The power problems of unit root test in time series with autoregressive errors," Journal of Econometrics, Elsevier, vol. 53(1-3), pages 323-343.
  5. Yoosoon Chang & Joon Y. Park, 2003. "A Sieve Bootstrap For The Test Of A Unit Root," Journal of Time Series Analysis, Wiley Blackwell, vol. 24(4), pages 379-400, 07.
  6. Domowitz, Ian & El-Gamal, Mahmoud A., 2001. "A consistent nonparametric test of ergodicity for time series with applications," Journal of Econometrics, Elsevier, vol. 102(2), pages 365-398, June.
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Cited by:
  1. Chang, Yoosoon, 2002. "Bootstrap Unit Root Tests in Panels with Cross-Sectional Dependency," Working Papers 2000-01, Rice University, Department of Economics.
  2. Chang, Yoosoon, 2003. "Nonlinear IV Panel Unit Root Tests," Working Papers 2003-06, Rice University, Department of Economics.
  3. Omtzigt Pieter & Fachin Stefano, 2002. "Bootstrapping and Bartlett corrections in the cointegrated VAR model," Economics and Quantitative Methods qf0212, Department of Economics, University of Insubria.

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