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Local Whittle Estimation in Nonstationary and Unit Root Cases

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Abstract

Asymptotic properties of the local Whittle estimator in the nonstationary case (d > 1/2) are explored. For 1/2 1 and when the process has a linear trend, the estimator is shown to be inconsistent and to converge in probability to unity.

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File URL: http://cowles.econ.yale.edu/P/cd/d12b/d1266.pdf
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Bibliographic Info

Paper provided by Cowles Foundation for Research in Economics, Yale University in its series Cowles Foundation Discussion Papers with number 1266.

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Length: 33 pages
Date of creation: Jul 2000
Date of revision: Sep 2003
Publication status: Published in The Annals of Statistics (2004), 34(2): 656-692
Handle: RePEc:cwl:cwldpp:1266

Note: CFP 1098
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Postal: Cowles Foundation, Yale University, Box 208281, New Haven, CT 06520-8281 USA

Related research

Keywords: Discrete Fourier transform; fractional Brownian motion; fractional integration; long memory; nonstationarity; semiparametric estimation; trend; Whittle likelihood; unit root;

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References

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  1. Katsumi Shimotsu & Peter C.B. Phillips, 2002. "Exact Local Whittle Estimation of Fractional Integration," Economics Discussion Papers 535, University of Essex, Department of Economics.
  2. Dean Corbae & Sam Ouliaris & Peter C. B. Phillips, 2002. "Band Spectral Regression with Trending Data," Econometrica, Econometric Society, vol. 70(3), pages 1067-1109, May.
  3. D. Marinucci & Peter M. Robinson, 2001. "Narrow-band analysis of nonstationary processes," LSE Research Online Documents on Economics 303, London School of Economics and Political Science, LSE Library.
  4. Peter C. Schotman & Herman K. van Dijk, 1991. "On Bayesian routes to unit roots," Discussion Paper / Institute for Empirical Macroeconomics 43, Federal Reserve Bank of Minneapolis.
  5. 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.
  6. D Marinucci & Peter M Robinson, 2001. "Narrow-Band Analysis of Nonstationary Processes," STICERD - Econometrics Paper Series /2001/421, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
  7. Phillips, Peter C.B., 2007. "Unit root log periodogram regression," Journal of Econometrics, Elsevier, vol. 138(1), pages 104-124, May.
  8. 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.
  9. Carlos Velasco, 2003. "Gaussian Semi-parametric Estimation of Fractional Cointegration," Journal of Time Series Analysis, Wiley Blackwell, vol. 24(3), pages 345-378, 05.
  10. Chang Sik Kim & Peter C.B. Phillips, 2006. "Log Periodogram Regression: The Nonstationary Case," Cowles Foundation Discussion Papers 1587, Cowles Foundation for Research in Economics, Yale University.
  11. Donald W.K. Andrews & Yixiao Sun, 2001. "Local Polynomial Whittle Estimation of Long-range Dependence," Cowles Foundation Discussion Papers 1293, Cowles Foundation for Research in Economics, Yale University.
  12. Peter C.B. Phillips, 1999. "Discrete Fourier Transforms of Fractional Processes," Cowles Foundation Discussion Papers 1243, Cowles Foundation for Research in Economics, Yale University.
  13. D Marinucci & Peter Robinson, 2001. "Narrow-band analysis of nonstationary processes," LSE Research Online Documents on Economics 2015, London School of Economics and Political Science, LSE Library.
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