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Efficient Tests for an Autoregressive Unit Root

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  • Elliott, Graham
  • Rothenberg, Thomas J
  • Stock, James H

Abstract

The asymptotic power envelope is derived for point-optimal tests of a unit root in the autoregressive representation of a Gaussian time series. The authors propose a family of tests whose asymptotic power functions are tangent to the power envelope at one point and are never far below. When the series has an unknown mean or linear trend, commonly used tests are found to be dominated by members of the family of point-optimal invariant tests. The authors propose a modified version of the Dickey-Fuller t test which has desirable size properties and substantially improved power when an unknown mean or trend is present. Copyright 1996 by The Econometric Society.

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Bibliographic Info

Article provided by Econometric Society in its journal Econometrica.

Volume (Year): 64 (1996)
Issue (Month): 4 (July)
Pages: 813-36

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Handle: RePEc:ecm:emetrp:v:64:y:1996:i:4:p:813-36

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  1. 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.
  2. Schwert, G William, 2002. "Tests for Unit Roots: A Monte Carlo Investigation," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 5-17, January.
  3. Baillie, Richard T & Bollerslev, Tim, 2002. "The Message in Daily Exchange Rates: A Conditional-Variance Tale," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 60-68, January.
  4. 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.
  5. Evans, G B A & Savin, N E, 1981. "Testing for Unit Roots: 1," Econometrica, Econometric Society, vol. 49(3), pages 753-79, May.
  6. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March.
  7. DeJong, David N. & Nankervis, John C. & Savin, N. E. & Whiteman, Charles H., 1992. "The power problems of unit root test in time series with autoregressive errors," Journal of Econometrics, Elsevier, vol. 53(1-3), pages 323-343.
  8. Schmidt, P. & Phillips, P.C.B., 1990. "Testing forUnit Root in the Presence of Deterministic Trends," Papers 8904, Michigan State - Econometrics and Economic Theory.
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