Taking a New Contour: A Novel View on Unit Root Test
In this paper we introduce a new view on the distributions of unit root tests. Taking a contour given by the fixed sum of squares instead of the fixed sample size, we show that the null distributions of most commonly used unit root tests such as the ones by Dickey-Fuller (1979, 1981) and Phillips (1987) are normal in large samples. The normal asymptotics along the new contour continue to hold under the local-to-unity alternatives, in which case the tests have normal limit distributions with mean given by the product of the square root of the level of the contour and the locality parameter. Our results are derived for the general unit root models with innovations satisfying the functional central limit theory that is routinely employed to obtain the unit root asymptotics. Moreover, the new asymptotics are shown to be applicable also for the models with deterministic components, as long as they are removed recursively by using only the past information.
|Date of creation:||Dec 2004|
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- Evans, G B A & Savin, N E, 1981. "Testing for Unit Roots: 1," Econometrica, Econometric Society, vol. 49(3), pages 753-79, May.
- 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.
- Chang, Yoosoon, 2002.
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- Yoosoon Chang, 2000. "Nonlinear IV Unit Root Tests in Panels with Cross-Sectional Dependency," CIRJE F-Series CIRJE-F-85, CIRJE, Faculty of Economics, University of Tokyo.
- Chang, Yoosoon, 2002. "Nonlinear IV Unit Root Tests in Panels with Cross-Sectional Dependency," Working Papers 2000-08, Rice University, Department of Economics.
- So, Beong Soo & Shin, Dong Wan, 1999. "Recursive mean adjustment in time-series inferences," Statistics & Probability Letters, Elsevier, vol. 43(1), pages 65-73, May.
- Evans, G B A & Savin, N E, 1984. "Testing for Unit Roots: 2," Econometrica, Econometric Society, vol. 52(5), pages 1241-69, September.
- 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.
- Yoosoon Chang & Joon Park, 2002. "On The Asymptotics Of Adf Tests For Unit Roots," Econometric Reviews, Taylor & Francis Journals, vol. 21(4), pages 431-447.
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