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

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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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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  1. 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.
  2. Granger, C. W. J. & Newbold, P., 1974. "Spurious regressions in econometrics," Journal of Econometrics, Elsevier, vol. 2(2), pages 111-120, July.
  3. 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.
  4. 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.
  5. 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.
  6. 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.
  7. Perron, Pierre, 1988. "Trends and random walks in macroeconomic time series : Further evidence from a new approach," Journal of Economic Dynamics and Control, Elsevier, vol. 12(2-3), pages 297-332.
  8. 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.
  9. 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.
  10. Schwert, G William, 1989. "Tests for Unit Roots: A Monte Carlo Investigation," Journal of Business & Economic Statistics, American Statistical Association, vol. 7(2), pages 147-59, April.
  11. 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.
  12. Evans, G B A & Savin, N E, 1984. "Testing for Unit Roots: 2," Econometrica, Econometric Society, vol. 52(5), pages 1241-69, September.
  13. Guilkey, David K. & Schmidt, Peter, 1989. "Extended tabulations for Dickey-Fuller tests," Economics Letters, Elsevier, vol. 31(4), pages 355-357, December.
  14. 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.
  15. 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.
  16. 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.
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