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Trend stationarity versus long-range dependence in time series analysis

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  • Marmol, Francesc
  • Velasco, Carlos

Abstract

Empirically, it is difficult to offer unequivocal judgment as to whether many real economic variables are fractionally integrated or trend stationary. The objective of this paper is to study the effects of spurious detrending of a nonstationary fractionally integrated NFI(d), dE (1/2, 3/2). With respect to the performance of the traditional least squares estimators and tests we prove that the estimated time trend coefficient is consistent but that the corresponding t-Student test diverges. We also analyze a local version in the frequency domain of least squares. We are able to show the consistency of this estimator and that, after conveniently adjusting variance estimates, its t-ratio has a well-defined but nonstandard limiting distribution. Nonetheless, in this latter case it is possible to obtain a set of critical values giving rise to the correct size for any given dE (1/2, 3/2).

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Econometrics.

Volume (Year): 108 (2002)
Issue (Month): 1 (May)
Pages: 25-42

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Handle: RePEc:eee:econom:v:108:y:2002:i:1:p:25-42

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Web page: http://www.elsevier.com/locate/jeconom

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References

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  1. Velasco, Carlos, . "Non-stationary log-periodogram regression," Open Access publications from Universidad Carlos III de Madrid info:hdl:10016/4554, Universidad Carlos III de Madrid.
  2. Steven N. Durlauf & Peter C.B. Phillips, 1986. "Trends Versus Random Walks in Time Series Analysis," Cowles Foundation Discussion Papers 788, Cowles Foundation for Research in Economics, Yale University.
  3. P.M. Robinson & D. Marinucci, 2000. "The Averaged Periodogram for Nonstationary Vector Time Series," Statistical Inference for Stochastic Processes, Springer, vol. 3(1), pages 149-160, January.
  4. Hassler, U. & Marmol, Francesc & Velasco, Carlos, . "Residual log-periodogram inference for long-run relationships," Open Access publications from Universidad Carlos III de Madrid info:hdl:10016/4359, Universidad Carlos III de Madrid.
  5. Velasco, Carlos, . "Gaussian Semiparametric Estimation of Non-stationary Time Series," Open Access publications from Universidad Carlos III de Madrid info:hdl:10016/4345, Universidad Carlos III de Madrid.
  6. Robinson, P.M. & Velasco, Carlos, . "Autocorrelation-Robust Inference," Open Access publications from Universidad Carlos III de Madrid info:hdl:10016/4529, Universidad Carlos III de Madrid.
  7. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March.
  8. Baillie, Richard T., 1996. "Long memory processes and fractional integration in econometrics," Journal of Econometrics, Elsevier, vol. 73(1), pages 5-59, July.
  9. Chambers, Marcus J., 1996. "Fractional integration, trend stationarity and difference stationarity Evidence from some U.K. macroeconomic time series," Economics Letters, Elsevier, vol. 50(1), pages 19-24, January.
  10. P. M. Robinson, 1998. "Inference-Without-Smoothing in the Presence of Nonparametric Autocorrelation," Econometrica, Econometric Society, vol. 66(5), pages 1163-1182, September.
  11. D Marinucci & Peter M Robinson, 2000. "The Averaged Periodogram for Nonstationary Vector Time Series," STICERD - Econometrics Paper Series /2000/408, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
  12. Marinucci, D. & Robinson, P. M., 2000. "Weak convergence of multivariate fractional processes," Stochastic Processes and their Applications, Elsevier, vol. 86(1), pages 103-120, March.
  13. Marmol, Francesc, 1998. "Spurious regression theory with nonstationary fractionally integrated processes," Journal of Econometrics, Elsevier, vol. 84(2), pages 233-250, June.
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Citations

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Cited by:
  1. Francesc, Marmol & Velasco, Carlos, . "Consistent testing of cointegrating relationships," Open Access publications from Universidad Carlos III de Madrid info:hdl:10016/4415, Universidad Carlos III de Madrid.
  2. Gilles Dufrénot & Valérie Mignon & Théo Naccache, . "The slow convergence of per capita income between the developing countries: “growth resistance” and sometimes “growth tragedy”," Discussion Papers 09/03, University of Nottingham, CREDIT.
  3. Arielle Beyaert, 2004. "Fractional Output Convergence, with an Application to Nine Developed Countries," Econometric Society 2004 Australasian Meetings 280, Econometric Society.
  4. Dolado, Juan José & Gonzalo, Jesús & Mayoral, Laura, . "What is What?: A Simple Time-Domain Test of Long-memory vs. Structural Breaks," Open Access publications from Universidad Carlos III de Madrid info:hdl:10016/3239, Universidad Carlos III de Madrid.
  5. Mohamed Boutahar, 2006. "Limiting distribution of the least squaresestimates in polynomial regression with longmemory noises," Working Papers halshs-00409571, HAL.
  6. Laura Mayoral, 2006. "Is the Observed Persistence Spurious? A Test for Fractional Integration versus Short Memory and Structural Breaks," Working Papers 260, Barcelona Graduate School of Economics.
  7. Laura Mayoral, 2005. "Is the observed persistence spurious? A test for fractional integration versus short memory and structural breaks," Economics Working Papers 956, Department of Economics and Business, Universitat Pompeu Fabra.

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