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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. Peter C.B. Phillips, 1985. "Time Series Regression with a Unit Root," Cowles Foundation Discussion Papers, Cowles Foundation for Research in Economics, Yale University 740R, Cowles Foundation for Research in Economics, Yale University, revised Feb 1986.
  2. 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, Cambridge University Press, vol. 3(03), pages 387-408, June.
  3. Evans, G B A & Savin, N E, 1984. "Testing for Unit Roots: 2," Econometrica, Econometric Society, Econometric Society, vol. 52(5), pages 1241-69, September.
  4. Dolado, Juan J & Jenkinson, Tim & Sosvilla-Rivero, Simon, 1990. " Cointegration and Unit Roots," Journal of Economic Surveys, Wiley Blackwell, Wiley Blackwell, vol. 4(3), pages 249-73.
  5. Perron, P., 1986. "Trends and Random Walks in Macroeconomic Time Series: Further Evidence From a New Approach," Cahiers de recherche, Universite de Montreal, Departement de sciences economiques 8650, Universite de Montreal, Departement de sciences economiques.
  6. Nelson, Charles R & Kang, Heejoon, 1981. "Spurious Periodicity in Inappropriately Detrended Time Series," Econometrica, Econometric Society, Econometric Society, vol. 49(3), pages 741-51, May.
  7. Nankervis, J. C. & Savin, N. E., 1985. "Testing the autoregressive parameter with the t statistic," Journal of Econometrics, Elsevier, Elsevier, vol. 27(2), pages 143-161, February.
  8. Nelson, Charles R. & Plosser, Charles I., 1982. "Trends and random walks in macroeconmic time series : Some evidence and implications," Journal of Monetary Economics, Elsevier, Elsevier, vol. 10(2), pages 139-162.
  9. Guilkey, David K. & Schmidt, Peter, 1989. "Extended tabulations for Dickey-Fuller tests," Economics Letters, Elsevier, Elsevier, vol. 31(4), pages 355-357, December.
  10. Granger, C. W. J. & Newbold, P., 1974. "Spurious regressions in econometrics," Journal of Econometrics, Elsevier, Elsevier, vol. 2(2), pages 111-120, July.
  11. G. William Schwert, 1988. "Tests For Unit Roots: A Monte Carlo Investigation," NBER Technical Working Papers, National Bureau of Economic Research, Inc 0073, National Bureau of Economic Research, Inc.
  12. Phillips, P.C.B., 1986. "Testing for a Unit Root in Time Series Regression," Cahiers de recherche, Universite de Montreal, Departement de sciences economiques 8633, Universite de Montreal, Departement de sciences economiques.
  13. Ayat, Leila & Burridge, Peter, 2000. "Unit root tests in the presence of uncertainty about the non-stochastic trend," Journal of Econometrics, Elsevier, Elsevier, vol. 95(1), pages 71-96, March.
  14. Dickey, David A & Fuller, Wayne A, 1981. "Likelihood Ratio Statistics for Autoregressive Time Series with a Unit Root," Econometrica, Econometric Society, Econometric Society, vol. 49(4), pages 1057-72, June.
  15. Pantula, Sastry G. & Hall, Alastair, 1991. "Testing for unit roots in autoregressive moving average models : An instrumental variable approach," Journal of Econometrics, Elsevier, Elsevier, vol. 48(3), pages 325-353, June.
  16. 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, Department of Economics, University of Oxford, vol. 54(3), pages 349-67, August.
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Citations

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Cited by:
  1. Hallin, Marc & van den Akker, Ramon & Werker, Bas J.M., 2011. "A class of simple distribution-free rank-based unit root tests," Journal of Econometrics, Elsevier, Elsevier, vol. 163(2), pages 200-214, August.
  2. 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, Tilburg University, Center for Economic Research 2010-72, Tilburg University, Center for Economic Research.
  3. Marc Hallin & Ramon van den Akker & Bas Werker, 2009. "A class of Simple Semiparametrically Efficient Rank-Based Unit Root Tests," Working Papers ECARES, ULB -- Universite Libre de Bruxelles 2009_001, ULB -- Universite Libre de Bruxelles.
  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, Tilburg University, Center for Economic Research 2011-002, Tilburg University, Center for Economic Research.

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