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Testing I(1) against I(d) alternatives in the presence of deteministic components

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Author Info
Juan J. Dolado
Jesús Gonzalo
Laura Mayoral ()

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Abstract

This paper discusses the role of deterministic components in the DGP and in the auxiliary regression model which underlies the implementation of the Fractional Dickey-Fuller (FDF) test for I(1) against I(d) processes with d € [0, 1). This is an important test in many economic applications because I(d) processess with d < 1 are mean-reverting although, when 0.5 = d < 1, like I(1) processes, they are nonstationary. We show how simple is the implementation of the FDF in these situations, and argue that it has better properties than LM tests. A simple testing strategy entailing only asymptotically normally distributed tests is also proposed. Finally, an empirical application is provided where the FDF test allowing for deterministic components is used to test for long-memory in the per capita GDP of several OECD countries, an issue that has important consequences to discriminate between growth theories, and on which there is some controversy.

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Paper provided by Department of Economics and Business, Universitat Pompeu Fabra in its series Economics Working Papers with number 957.

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Date of creation: Feb 2005
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Handle: RePEc:upf:upfgen:957

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Related research
Keywords: Deterministic components; Dickey-Fuller test; fractionally Dickey-Fuller test; fractional processes; long memory; trends; unit roots;

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Find related papers by JEL classification:
C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Hypothesis Testing
C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions
C40 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - General

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References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. 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. [Downloadable!] (restricted)
  2. Michelacci, C. & Zaffaroni, P., 2000. "(Fractional) Beta Convergence," Papers 383, Banca Italia - Servizio di Studi.
    Other versions:
  3. Velasco, Carlos, 1999. "Non-stationary log-periodogram regression," Journal of Econometrics, Elsevier, vol. 91(2), pages 325-371, August. [Downloadable!] (restricted)
  4. Peter M Robinson & Carlos Velasco, 2000. "Whittle Pseudo-Maximum Likelihood Estimation for Nonstationary Time Series - (Now published in Journal of the American Statistical Association, 95, (2000), pp.1229-1243.)," STICERD - Econometrics Paper Series /2000/391, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE. [Downloadable!]
  5. Tanaka, Katsuto, 1999. "The Nonstationary Fractional Unit Root," Econometric Theory, Cambridge University Press, vol. 15(04), pages 549-582, August. [Downloadable!]
  6. Baillie, Richard T., 1996. "Long memory processes and fractional integration in econometrics," Journal of Econometrics, Elsevier, vol. 73(1), pages 5-59, July. [Downloadable!] (restricted)
  7. Joerg Breitung and Uwe Hassler, 2001. "Inference on the Cointegration Rank in Fractionally Integrated Processes," Computing in Economics and Finance 2001 233, Society for Computational Economics.
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  8. Hylleberg, Svend & Mizon, Grayham E., 1989. "A note on the distribution of the least squares estimator of a random walk with drift," Economics Letters, Elsevier, vol. 29(3), pages 225-230. [Downloadable!] (restricted)
  9. Juan J. Dolado & Francesc Marmol, 2004. "Asymptotic inference results for multivariate long-memory processes," Econometrics Journal, Royal Economic Society, vol. 7(1), pages 168-190, 06. [Downloadable!] (restricted)
  10. Liu, Ming, 1998. "Asymptotics Of Nonstationary Fractional Integrated Series," Econometric Theory, Cambridge University Press, vol. 14(05), pages 641-662, October. [Downloadable!]
  11. Jones, Charles I, 1995. "Time Series Tests of Endogenous Growth Models," The Quarterly Journal of Economics, MIT Press, vol. 110(2), pages 495-525, May. [Downloadable!] (restricted)
  12. Ignacio N. Lobato & Carlos Velasco, 2004. "Optimal Fractional Dickey-Fuller Tests for Unit Roots," Working Papers 0401, Centro de Investigacion Economica, ITAM. [Downloadable!]
  13. West, Kenneth D, 1988. "Asymptotic Normality, When Regressors Have a Unit Root," Econometrica, Econometric Society, vol. 56(6), pages 1397-1417, November. [Downloadable!] (restricted)
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Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Laura Mayoral, 2005. "Further evidence on the statistical properties of Real GNP," Economics Working Papers 955, Department of Economics and Business, Universitat Pompeu Fabra, revised Feb 2006. [Downloadable!]
    Other versions:
  2. Derek Bond & Michael J. Harrison & Edward J. O'Brien, 2007. "Demand for Money: A Study in Testing Time Series for Long Memory and Nonlinearity," The Economic and Social Review, Economic and Social Studies, vol. 38(1), pages 1-24. [Downloadable!]
  3. Laura Mayoral, 2006. "Minimum Distance Estimation of stationary and non-stationary ARFIMA Processes," Economics Working Papers 959, Department of Economics and Business, Universitat Pompeu Fabra. [Downloadable!]
    Other versions:
  4. Peter Sephton, 2008. "Critical values of the augmented fractional Dickey–Fuller test," Empirical Economics, Springer, vol. 35(3), pages 437-450, November. [Downloadable!] (restricted)
  5. Juan J. Dolado & Jesús Gonzalo & Laura Mayoral, 2005. "What is What?: A Simple Time-Domain Test of Long-memory vs. Structural Breaks," Economics Working Papers 954, Department of Economics and Business, Universitat Pompeu Fabra. [Downloadable!]
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