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Testing for a Deterministic Trend When There is Evidence of Unit Root

  • Ventosa-Santaulària Daniel

    (Universidad de Guanajuato)

  • Gómez-Zaldívar Manuel

    (Universidad de Guanajuato)

Whilst the existence of a unit root implies that current shocks have permanent effects, in the long run, the simultaneous presence of a deterministic trend obliterates that consequence. As such, the long-run level of macroeconomic series depends upon the existence of a deterministic trend. This paper proposes a formal statistical procedure to distinguish between the null hypothesis of unit root and that of unit root with drift. Our procedure is asymptotically robust with regard to autocorrelation and takes into account a potential single structural break. Empirical results show that most of the macroeconomic time series originally analyzed by Nelson and Plosser (1982) are characterized by their containing both a deterministic and a stochastic trend.

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Article provided by De Gruyter in its journal Journal of Time Series Econometrics.

Volume (Year): 2 (2011)
Issue (Month): 2 (January)
Pages: 1-26

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Handle: RePEc:bpj:jtsmet:v:2:y:2011:i:2:n:3
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  1. Phillips, P.C.B., 1986. "Understanding spurious regressions in econometrics," Journal of Econometrics, Elsevier, vol. 33(3), pages 311-340, December.
  2. Lawrence J. Christiano, 1988. "Searching For a Break in GNP," NBER Working Papers 2695, National Bureau of Economic Research, Inc.
  3. Zivot, Eric & Andrews, Donald W K, 1992. "Further Evidence on the Great Crash, the Oil-Price Shock, and the Unit-Root Hypothesis," Journal of Business & Economic Statistics, American Statistical Association, vol. 10(3), pages 251-70, July.
  4. Vogelsang, T.J. & Perron, P., 1994. "Additional Tests for a Unit Root Allowing for a Break in the Trend Function at an Unknown Time," Cahiers de recherche 9422, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
  5. Carrion-i-Silvestre, Josep Lluís & Kim, Dukpa & Perron, Pierre, 2009. "Gls-Based Unit Root Tests With Multiple Structural Breaks Under Both The Null And The Alternative Hypotheses," Econometric Theory, Cambridge University Press, vol. 25(06), pages 1754-1792, December.
  6. Perron, Pierre, 1989. "The Great Crash, the Oil Price Shock, and the Unit Root Hypothesis," Econometrica, Econometric Society, vol. 57(6), pages 1361-1401, November.
  7. Perron, Pierre & Zhu, Xiaokang, 2005. "Structural breaks with deterministic and stochastic trends," Journal of Econometrics, Elsevier, vol. 129(1-2), pages 65-119.
  8. Kim, Dukpa & Perron, Pierre, 2009. "Unit root tests allowing for a break in the trend function at an unknown time under both the null and alternative hypotheses," Journal of Econometrics, Elsevier, vol. 148(1), pages 1-13, January.
  9. 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.
  10. Gómez, Manuel & Ventosa-Santaulària, Daniel, 2007. "Income convergence: the Dickey-Fuller test under the simultaneous presence of stochastic and deterministic trends," MPRA Paper 58778, University Library of Munich, Germany.
  11. Josep Llu�s Carrion-i-Silvestre & Andreu Sans�, 2006. "Joint hypothesis specification for unit root tests with a structural break *," Econometrics Journal, Royal Economic Society, vol. 9(2), pages 196-224, 07.
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