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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.

Suggested Citation

  • Ventosa-Santaulària Daniel & Gómez-Zaldívar Manuel, 2011. "Testing for a Deterministic Trend When There is Evidence of Unit Root," Journal of Time Series Econometrics, De Gruyter, vol. 2(2), pages 1-26, January.
  • Handle: RePEc:bpj:jtsmet:v:2:y:2011:i:2:n:3

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    References listed on IDEAS

    1. 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.
    2. P. C. B. Phillips & S. N. Durlauf, 1986. "Multiple Time Series Regression with Integrated Processes," Review of Economic Studies, Oxford University Press, vol. 53(4), pages 473-495.
    3. Christiano, Lawrence J, 1992. "Searching for a Break in GNP," Journal of Business & Economic Statistics, American Statistical Association, vol. 10(3), pages 237-250, July.
    4. Manuel Gomez & Daniel Ventosa-Santaularia, 2007. "Income Convergence: The Dickey-Fuller Test under the Simultaneous Presence of Stochastic and Deterministic Trends," Department of Economics and Finance Working Papers EM200703, Universidad de Guanajuato, Department of Economics and Finance.
    5. Josep Lluís Carrion-i-Silvestre & Andreu Sansó, 2006. "Joint hypothesis specification for unit root tests with a structural break *," Econometrics Journal, Royal Economic Society, vol. 9(2), pages 196-224, July.
    6. Perron, Pierre & Zhu, Xiaokang, 2005. "Structural breaks with deterministic and stochastic trends," Journal of Econometrics, Elsevier, vol. 129(1-2), pages 65-119.
    7. Manuel Gomez-Zaldivar & Daniel Ventosa-Santaularia, 2010. "Per Capita Output Convergence : The Dickey-Fuller Test Under the Simultaneous Presence of Stochastic and Deterministic Trends," Annals of Economics and Statistics, GENES, issue 99-100, pages 429-445.
    8. Zivot, Eric & Andrews, Donald W K, 2002. "Further Evidence on the Great Crash, the Oil-Price Shock, and the Unit-Root Hypothesis," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 25-44, January.
    9. Vogelsang, Timothy J & Perron, Pierre, 1998. "Additional Tests for a Unit Root Allowing for a Break in the Trend Function at an Unknown Time," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 1073-1100, November.
    10. Phillips, P.C.B., 1986. "Understanding spurious regressions in econometrics," Journal of Econometrics, Elsevier, vol. 33(3), pages 311-340, December.
    11. 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.
    12. 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.
    13. 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.
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    Cited by:

    1. Gomez Zaldivar, M. & Ventosa-Santaularia, D., 2009. "Bilateral Relationship between Consumption and GDP in Mexico and the USA: A Comment," Applied Econometrics and International Development, Euro-American Association of Economic Development, vol. 9(1).
    2. Rodríguez-Caballero, Carlos Vladimir & Ventosa-Santaulària, Daniel, 2017. "Energy-growth long-term relationship under structural breaks. Evidence from Canada, 17 Latin American economies and the USA," Energy Economics, Elsevier, vol. 61(C), pages 121-134.
    3. Felipe J. Fonseca & Daniel Ventosa-Santaulària, 2011. "Revenue Elasticity of the Main federal Taxes in Mexico," Latin American Journal of Economics-formerly Cuadernos de Economía, Instituto de Economía. Pontificia Universidad Católica de Chile., vol. 48(1), pages 89-111.
    4. Daniel Ventosa-santaulària & Manuel Gómez-zaldívar & Lizet A Pérez, 2013. "Long-run relationship with shifts between Mexican current account revenues and expenditures," Economics Bulletin, AccessEcon, vol. 33(2), pages 1317-1327.
    5. Víctor-Hugo Alcalá Ríos & Manuel Gómez Zaldívar & Daniel Ventosa-Santaulària, 2011. "Paradoja Feldstein-Horioka: el caso de México (1950-2007)," Estudios Económicos, El Colegio de México, Centro de Estudios Económicos, vol. 26(2), pages 293-313.

    More about this item

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • E30 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - General (includes Measurement and Data)


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