The Available Information for Invariant Tests of a Unit Root
This paper considers the information available to invariant unit root tests at and near the unit root. Since all invariant tests will be functions of the maximal invariant, the Fisher information in this statistic will be the available information. The main finding of the paper is that the available information for all tests invariant to a linear trend is zero at the unit root. This result applies for any sample size, over a variety of distributions and correlation structures and is robust to the inclusion of any other deterministic component. In addition, an explicit bound upon the power of all invariant unit root tests is shown to depend solely upon the information. This bound is illustrated via comparison with the local-to-unity power envelope and a brief simulation study illustrates the impact that the requirements of invariance have on power.
|Date of creation:|
|Date of revision:|
|Contact details of provider:|| Postal: |
Phone: (0)1904 323776
Fax: (0)1904 323759
Web page: http://www.york.ac.uk/economics/
More information through EDIRC
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.:
- Abadir, Karim M., 1993. "On the Asymptotic Power of Unit Root Tests," Econometric Theory, Cambridge University Press, vol. 9(02), pages 189-221, April.
- Steven N. Durlauf & Peter C.B. Phillips, 1986.
"Trends Versus Random Walks in Time Series Analysis,"
Cowles Foundation Discussion Papers
788, Cowles Foundation for Research in Economics, Yale University.
- Durlauf, Steven N & Phillips, Peter C B, 1988. "Trends versus Random Walks in Time Series Analysis," Econometrica, Econometric Society, vol. 56(6), pages 1333-54, November.
- 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.
- 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.
- Bunzel, Helle & Vogelsang, Timothy J., 2003.
"Powerful Trend Function Tests That Are Robust to Strong Serial Correlation with an Application to the Prebisch-Singer Hypothesis,"
Staff General Research Papers
10353, Iowa State University, Department of Economics.
- Bunzel, Helle & Vogelsang, Timothy J., 2005. "Powerful Trend Function Tests That Are Robust to Strong Serial Correlation, With an Application to the Prebisch-Singer Hypothesis," Journal of Business & Economic Statistics, American Statistical Association, vol. 23, pages 381-394, October.
- Helle Bunzel & Timothy Vogelsang, 2003. "Powerful Trend Function Tests That are Robust to Strong Serial Correlation with an Application to the Prebisch Singer Hypothesis," Econometrics 0304002, EconWPA.
- Leybourne, Stephen J. & C. Mills, Terence & Newbold, Paul, 1998. "Spurious rejections by Dickey-Fuller tests in the presence of a break under the null," Journal of Econometrics, Elsevier, vol. 87(1), pages 191-203, August.
- DeJong, David N, et al, 1992. "Integration versus Trend Stationarity in Time Series," Econometrica, Econometric Society, vol. 60(2), pages 423-33, March.
- Werner Ploberger & Peter C.B. Phillips, 1998. "Rissanen's Theorem and Econometric Time Series," Cowles Foundation Discussion Papers 1197, Cowles Foundation for Research in Economics, Yale University.
- Giovanni Forchini & Patrick Marsh, . "Exact Inference for the Unit Root Hypothesis," Discussion Papers 00/54, Department of Economics, University of York.
- 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.
- Dufour, Jean-Marie & King, Maxwell L., 1991. "Optimal invariant tests for the autocorrelation coefficient in linear regressions with stationary or nonstationary AR(1) errors," Journal of Econometrics, Elsevier, vol. 47(1), pages 115-143, January.
- Timothy J. Vogelsang, 1998. "Trend Function Hypothesis Testing in the Presence of Serial Correlation," Econometrica, Econometric Society, vol. 66(1), pages 123-148, January.
When requesting a correction, please mention this item's handle: RePEc:yor:yorken:05/03. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Paul Hodgson)
If references are entirely missing, you can add them using this form.