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Semiparametric Power Envelopes for Tests of the Unit Root Hypothesis

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Author Info
Michael Jansson () (School of Economics and Management, University of Aarhus, Denmark and CREATES)

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Abstract

This paper derives asymptotic power envelopes for tests of the unit root hypothesis in a zero-mean AR(1) model. The power envelopes are derived using the limits of experiments approach and are semiparametric in the sense that the underlying error distribution is treated as an unknown infinitedimensional nuisance parameter. Adaptation is shown to be possible when the error distribution is known to be symmetric and to be impossible when the error distribution is unrestricted. In the latter case, two conceptually distinct approaches to nuisance parameter elimination are employed in the derivation of the semiparametric power bounds. One of these bounds, derived under an invariance restriction, is shown by example to be sharp, while the other, derived under a similarity restriction, is conjectured not to be globally attainable.

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Paper provided by School of Economics and Management, University of Aarhus in its series CREATES Research Papers with number 2007-12.

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Length: 50
Date of creation: 25 Jun 2007
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Handle: RePEc:aah:create:2007-12

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Related research
Keywords: Unit root testing; semiparametric efficiency;

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Find related papers by JEL classification:
C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Semiparametric and Nonparametric Methods
C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions

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References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Ulrich K. M¸ller & Graham Elliott, 2003. "Tests for Unit Roots and the Initial Condition," Econometrica, Econometric Society, vol. 71(4), pages 1269-1286, 07. [Downloadable!] (restricted)
  2. 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. [Downloadable!] (restricted)
  3. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March. [Downloadable!] (restricted)
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  4. Shiqing Ling & Michael McAleer, 2001. "On Adaptive Estimation in Nonstationary ARMA Models with GARCH Errors," ISER Discussion Paper 0548, Institute of Social and Economic Research, Osaka University. [Downloadable!]
  5. Stock, James H & Watson, Mark W, 1993. "A Simple Estimator of Cointegrating Vectors in Higher Order Integrated Systems," Econometrica, Econometric Society, vol. 61(4), pages 783-820, July. [Downloadable!] (restricted)
    Other versions:
  6. Phillips, Peter C B & Xiao, Zhijie, 1998. " A Primer on Unit Root Testing," Journal of Economic Surveys, Blackwell Publishing, vol. 12(5), pages 423-69, December. [Downloadable!] (restricted)
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  7. Newey, Whitney K, 1990. "Semiparametric Efficiency Bounds," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 5(2), pages 99-135, April-Jun. [Downloadable!] (restricted)
  8. Rothenberg, Thomas J. & Stock, James H., 1997. "Inference in a nearly integrated autoregressive model with nonnormal innovations," Journal of Econometrics, Elsevier, vol. 80(2), pages 269-286, October. [Downloadable!] (restricted)
  9. Perron, Pierre & Ng, Serena, 1996. "Useful Modifications to Some Unit Root Tests with Dependent Errors and Their Local Asymptotic Properties," Review of Economic Studies, Blackwell Publishing, vol. 63(3), pages 435-63, July. [Downloadable!] (restricted)
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  10. 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. [Downloadable!] (restricted)
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  11. Serena Ng & Pierre Perron, 2001. "LAG Length Selection and the Construction of Unit Root Tests with Good Size and Power," Econometrica, Econometric Society, vol. 69(6), pages 1519-1554, November. [Downloadable!] (restricted)
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  12. Jeganathan, P., 1995. "Some Aspects of Asymptotic Theory with Applications to Time Series Models," Econometric Theory, Cambridge University Press, vol. 11(05), pages 818-887, October. [Downloadable!]
  13. Keisuke Hirano & Jack R. Porter, 2003. "Asymptotic Efficiency in Parametric Structural Models with Parameter-Dependent Support," Econometrica, Econometric Society, vol. 71(5), pages 1307-1338, 09. [Downloadable!] (restricted)
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  14. Joon Y. Park, 2003. "Bootstrap Unit Root Tests," Econometrica, Econometric Society, vol. 71(6), pages 1845-1895, November. [Downloadable!] (restricted)
  15. Roger Koenker & Zhijie Xiao, 2004. "Unit Root Quantile Autoregression Inference," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 775-787, January. [Downloadable!] (restricted)
  16. M. N. Hasan & R. W. Koenker, 1997. "Robust Rank Tests of the Unit Root Hypothesis," Econometrica, Econometric Society, vol. 65(1), pages 133-162, January.
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  19. Jeganathan, P., 1997. "On Asymptotic Inference in Linear Cointegrated Time Series Systems," Econometric Theory, Cambridge University Press, vol. 13(05), pages 692-745, October. [Downloadable!]
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Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Mathias D. Cattaneo & Richard K. Crump & Michael Jansson, 2007. "Optimal Inference for Instrumental Variables Regression with non-Gaussian Errors," CREATES Research Papers 2007-11, School of Economics and Management, University of Aarhus. [Downloadable!]
  2. Hallin, M. & Akker, R. van den & Werker, B.J.M., 2009. "A Class of Simple Semiparametrically Efficient Rank-Based Unit Root Tests," Discussion Paper 2009-2, Tilburg University, Center for Economic Research. [Downloadable!]
    Other versions:
  3. Joseph P. Romano & Azeem M. Shaikh & Michael Wolf, 2009. "Hypothesis testing in econometrics," IEW - Working Papers iewwp444, Institute for Empirical Research in Economics - IEW. [Downloadable!]
  4. Michael Jansson & Morten Ørregaard Nielsen, 2009. "Nearly Efficient Likelihood Ratio Tests of the Unit Root Hypothesis," CREATES Research Papers 2009-37, School of Economics and Management, University of Aarhus. [Downloadable!]
    Other versions:
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