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A Strategy for Testing the Unit Root in AR(1) Model with Intercept. A Monte Carlo Experiment

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Abstract

In this paper we introduce a strategy for testing the unit root hypothesis in a first-order autoregressive process with an unknown intercept where the initial value of the variable is a known constant. In the context of this model the standard Dickey-Fuller test is nonsimilar, the intercept being the nuisance parameter. The testing strategy we propose takes into account this non-similarity. It is an unusual two-sided test of the random walk hypothesis since it involves two distributions where the acceptance region is constructed by taking away equal areas for the lower tail of the Student’s t distribution and the upper tail of the distribution tabulated by Dickey and Fuller under the null hypothesis of unit root. In some cases, this strategy does not allow the taking of a direct decision concerning the existence of a unit root. To deal with these situations we suggest testing for the significance of the intercept, and if doubt continues, we use F1 test proposed by Dickey and Fuller (1981). Finally, in order to demonstrate the relevance of non-similarity, Monte Carlo simulations are used to show that the testing strategy is more powerful at stable alternatives and has less size distortions than the two-sided test considered by Dickey and Fuller.

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Bibliographic Info

Paper provided by Centro de Estudios Andaluces in its series Economic Working Papers at Centro de Estudios Andaluces with number E2004/37.

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Length: 37 pages
Date of creation: 2004
Date of revision:
Handle: RePEc:cea:doctra:e2004_37

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Keywords: unit root; Dickey-Fuller tests; non-similarity; Monte Carlo simulations; empirical size; nominal size;

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References

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  1. Nankervis, J. C. & Savin, N. E., 1985. "Testing the autoregressive parameter with the t statistic," Journal of Econometrics, Elsevier, vol. 27(2), pages 143-161, February.
  2. G. William Schwert, 1988. "Tests For Unit Roots: A Monte Carlo Investigation," NBER Technical Working Papers 0073, National Bureau of Economic Research, Inc.
  3. Nelson, Charles R. & Plosser, Charles I., 1982. "Trends and random walks in macroeconmic time series : Some evidence and implications," Journal of Monetary Economics, Elsevier, vol. 10(2), pages 139-162.
  4. Nelson, Charles R & Kang, Heejoon, 1979. "Spurious Periodicity in Inappropriately Detrended Time Series," The Warwick Economics Research Paper Series (TWERPS) 161, University of Warwick, Department of Economics.
  5. Evans, G B A & Savin, N E, 1984. "Testing for Unit Roots: 2," Econometrica, Econometric Society, vol. 52(5), pages 1241-69, September.
  6. Ayat, Leila & Burridge, Peter, 2000. "Unit root tests in the presence of uncertainty about the non-stochastic trend," Journal of Econometrics, Elsevier, vol. 95(1), pages 71-96, March.
  7. Nankervis, J.C. & Savin, N.E., 1987. "Finite Sample Distributions of t and F Statistics in an AR(1) Model with Anexogenous Variable," Econometric Theory, Cambridge University Press, vol. 3(03), pages 387-408, June.
  8. Perron, P., 1986. "Trends and Random Walks in Macroeconomic Time Series: Further Evidence From a New Approach," Cahiers de recherche 8650, Universite de Montreal, Departement de sciences economiques.
  9. Granger, C. W. J. & Newbold, P., 1974. "Spurious regressions in econometrics," Journal of Econometrics, Elsevier, vol. 2(2), pages 111-120, July.
  10. Phillips, P.C.B., 1986. "Testing for a Unit Root in Time Series Regression," Cahiers de recherche 8633, Universite de Montreal, Departement de sciences economiques.
  11. Kiviet, Jan F & Phillips, Garry D A, 1992. "Exact Similar Tests for Unit Roots and Cointegration," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 54(3), pages 349-67, August.
  12. Guilkey, David K. & Schmidt, Peter, 1989. "Extended tabulations for Dickey-Fuller tests," Economics Letters, Elsevier, vol. 31(4), pages 355-357, December.
  13. 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.
  14. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March.
  15. Dolado, Juan J & Jenkinson, Tim & Sosvilla-Rivero, Simon, 1990. " Cointegration and Unit Roots," Journal of Economic Surveys, Wiley Blackwell, vol. 4(3), pages 249-73.
  16. Pantula, Sastry G. & Hall, Alastair, 1991. "Testing for unit roots in autoregressive moving average models : An instrumental variable approach," Journal of Econometrics, Elsevier, vol. 48(3), pages 325-353, June.
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Citations

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Cited by:
  1. Marc Hallin & Ramon van den Akker & Bas Werker, 2009. "A class of Simple Semiparametrically Efficient Rank-Based Unit Root Tests," Working Papers ECARES 2009_001, ULB -- Universite Libre de Bruxelles.
  2. Marc Hallin & Ramon van den Akker & Bas J.M. Werker, 2011. "A class of simple distribution-free rank-based unit root tests," Post-Print hal-00834424, HAL.
  3. Hallin, M. & Akker, R. van den & Werker, B.J.M., 2010. "A Class of Simple Distribution-Free Rank-Based Unit Root Tests (Replaced by DP 2011-002)," Discussion Paper 2010-72, Tilburg University, Center for Economic Research.
  4. Hallin, M. & Akker, R. van den & Werker, B.J.M., 2011. "A Class of Simple Distribution-free Rank-based Unit Root Tests (Revision of DP 2010-72)," Discussion Paper 2011-002, Tilburg University, Center for Economic Research.

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