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Near-Optimal Unit Root Tests with Stationary Covariates with Better Finite Sample Size

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  • Elena Pesavento

Abstract

Numerous tests for integration and cointegration have been proposed in the literature. Since Elliott, Rothemberg and Stock (1996) the search for tests with better power has moved in the direction of finding tests with some optimality properties both in univariate and multivariate models. Although the optimal tests constructed so far have asymptotic power that is indistinguishable from the power envelope, it is well known that they can have severe size distortions in finite samples. This paper proposes a simple and powerful test that can be used to test for unit root or for no cointegration when the cointegration vector is known. Although this test is not optimal in the sense of Elliott and Jansson (2003), it has better finite sample size properties while having asymptotic power curves that are indistinguishable from the power curves of optimal tests. Similarly to Hansen (1995), Elliott and Jansson (2003), Zivot (2000), and Elliott, Jansson and Pesavento (2005) the proposed test achieves higher power by using additional information contained in covariates correlated with the variable being tested. The test is constructed by applying Hansen’s test to variables that are detrended under the alternative in a regression augmented with leads and lags of the stationary covariates. Using local to unity parametrization, the asymptotic distribution of the test under the null and the local alternative is analytically computed.

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Bibliographic Info

Paper provided by European University Institute in its series Economics Working Papers with number ECO2006/18.

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Date of creation: 2006
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Handle: RePEc:eui:euiwps:eco2006/18

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Keywords: Unit Root Test; GLS detrending.;

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References

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  1. Graham Elliott & Michael Jansson & Elena Pesavento, 2005. "Optimal Power for Testing Potential Cointegrating Vectors With Known Parameters for Nonstationarity," Journal of Business & Economic Statistics, American Statistical Association, vol. 23, pages 34-48, January.
  2. Pesavento, Elena & Rossi, Barbara, 2004. "Small Sample Confidence Intervals for Multivariate Impulse Response Functions at Long Horizons," CEPR Discussion Papers 4536, C.E.P.R. Discussion Papers.
  3. Bruce E. Hansen, 1995. "Rethinking the Univariate Approach to Unit Root Testing: Using Covariates to Increase Power," Boston College Working Papers in Economics 300., Boston College Department of Economics.
  4. Elliott, Graham & Jansson, Michael, 2002. "Testing for Unit Roots with Stationary Covariates," University of California at San Diego, Economics Working Paper Series qt4v35s2gv, Department of Economics, UC San Diego.
  5. Serena Ng & Pierre Perron, 1997. "Lag Length Selection and the Construction of Unit Root Tests with Good Size and Power," Boston College Working Papers in Economics 369, Boston College Department of Economics, revised 01 Sep 2000.
  6. Graham Elliott & Thomas J. Rothenberg & James H. Stock, 1992. "Efficient Tests for an Autoregressive Unit Root," NBER Technical Working Papers 0130, National Bureau of Economic Research, Inc.
  7. Barbara Rossi, 2007. "Expectations hypotheses tests at Long Horizons," Econometrics Journal, Royal Economic Society, vol. 10(3), pages 554-579, November.
  8. Rossi, Barbara, 2002. "Confidence Intervals for Half-life Deviations from Purchasing Power Parity," Working Papers 02-08, Duke University, Department of Economics.
  9. Michael Jansson & Marcelo J. Moreira, 2006. "Optimal Inference in Regression Models with Nearly Integrated Regressors," Econometrica, Econometric Society, vol. 74(3), pages 681-714, 05.
  10. Ng, S. & Perron, P., 1994. "Unit Root Tests ARMA Models with Data Dependent Methods for the Selection of the Truncation Lag," Cahiers de recherche 9423, Universite de Montreal, Departement de sciences economiques.
  11. Saikkonen, Pentti, 1991. "Asymptotically Efficient Estimation of Cointegration Regressions," Econometric Theory, Cambridge University Press, vol. 7(01), pages 1-21, March.
  12. Sims, Christopher A & Stock, James H & Watson, Mark W, 1990. "Inference in Linear Time Series Models with Some Unit Roots," Econometrica, Econometric Society, vol. 58(1), pages 113-44, January.
  13. Peter C.B. Phillips, 1986. "Towards a Unified Asymptotic Theory for Autoregression," Cowles Foundation Discussion Papers 782R, Cowles Foundation for Research in Economics, Yale University, revised Aug 1986.
  14. repec:cup:etheor:v:11:y:1995:i:5:p:1148-71 is not listed on IDEAS
  15. Peter C.B. Phillips & Victor Solo, 1989. "Asymptotics for Linear Processes," Cowles Foundation Discussion Papers 932, Cowles Foundation for Research in Economics, Yale University.
  16. repec:cup:etheor:v:7:y:1991:i:1:p:1-21 is not listed on IDEAS
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Cited by:
  1. Galvao Jr., Antonio F., 2009. "Unit root quantile autoregression testing using covariates," Journal of Econometrics, Elsevier, vol. 152(2), pages 165-178, October.
  2. Sebastian Fossati, 2013. "Unit root testing with stationary covariates and a structural break in the trend function," Journal of Time Series Analysis, Wiley Blackwell, vol. 34(3), pages 368-384, 05.
  3. Fossati, Sebastian, 2012. "Covariate unit root tests with good size and power," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3070-3079.
  4. Christopoulos, Dimitris K. & León-Ledesma, Miguel A., 2008. "Time-series output convergence tests and stationary covariates," Economics Letters, Elsevier, vol. 101(3), pages 297-299, December.

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