On the inconsistency of the unrestricted estimator of the information matrix near a unit root
The unrestricted estimator of the information matrix is shown to be inconsistent for an autoregressive process with a root lying in a neighbourhood of unity with radial length proportional or smaller than 1/n, i.e. a root that takes the form rho=1+c/n^alpha, alpha>=1. In this case the information evaluated at rho-hat_n converges to a non-degenerate random variable and contributes to the asymptotic distribution of a Wald test for the null hypothesis of a random walk versus a stable AR(1) alternative. With this newly derived asymptotic distribution the above Wald test is found to improve its performance. A non local criterion of asymptotic relative efficiency based on Bahadur slopes has been employed for the first time to the problem of unit root testing. The Wald test derived in the paper is found to be as efficient as the Dickey Fuller t ratio test and to outperform the non studentised Dickey Fuller test and a Lagrange Multiplier test.
|Date of creation:||Oct 2005|
|Date of revision:|
|Contact details of provider:|| Postal: School of Economics University of Nottingham University Park Nottingham NG7 2RD|
Phone: (44) 0115 951 5620
Fax: (0115) 951 4159
Web page: http://www.nottingham.ac.uk/research/groups/grangercentre/index.aspx
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.:
- 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.
- Liudas Giraitis & Peter C.B. Phillips, 2004.
"Uniform Limit Theory for Stationary Autoregression,"
Cowles Foundation Discussion Papers
1475, Cowles Foundation for Research in Economics, Yale University.
- Liudas Giraitis & Peter C. B. Phillips, 2006. "Uniform Limit Theory for Stationary Autoregression," Journal of Time Series Analysis, Wiley Blackwell, vol. 27(1), pages 51-60, 01.
- L Giraitis & P C B Phillips, . "Uniform limit theory for stationary autoregression," Discussion Papers 05/23, Department of Economics, University of York.
- Phillips, Peter C.B. & Magdalinos, Tassos, 2007.
"Limit theory for moderate deviations from a unit root,"
Journal of Econometrics,
Elsevier, vol. 136(1), pages 115-130, January.
- Peter C.B. Phillips & Tassos Magdalinos, 2004. "Limit Theory for Moderate Deviations from a Unit Root," Cowles Foundation Discussion Papers 1471, Cowles Foundation for Research in Economics, Yale University.
- Evans, G B A & Savin, N E, 1981. "Testing for Unit Roots: 1," Econometrica, Econometric Society, vol. 49(3), pages 753-79, May.
- Abadir, K.M., 1992.
"The Limiting Distribution of the T Ratio Under a Unit Root,"
1992-2, American Cairo - Economics and Political Sciences.
- Abadir, Karim M., 1995. "The Limiting Distribution of the t Ratio Under a Unit Root," Econometric Theory, Cambridge University Press, vol. 11(04), pages 775-793, August.
- Peter C.B. Phillips, 1985.
"Time Series Regression with a Unit Root,"
Cowles Foundation Discussion Papers
740R, Cowles Foundation for Research in Economics, Yale University, revised Feb 1986.
- Abadir, Karim M., 1993. "On the Asymptotic Power of Unit Root Tests," Econometric Theory, Cambridge University Press, vol. 9(02), pages 189-221, April.
When requesting a correction, please mention this item's handle: RePEc:not:notgts:06/05. 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: ()
If references are entirely missing, you can add them using this form.