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Local Whittle Estimation in Nonstationary and Unit Root Cases

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Author Info
Katsumi Shimotsu
Peter C.B. Phillips () (Cowles Foundation, Yale University)

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Abstract

Asymptotic properties of the local Whittle estimator in the nonstationary case (d > 1/2) are explored. For 1/2 < d < 1, the estimator is shown to be consistent, and its limit distribution and the rate of convergence depend on the value of d. For d = 1, the limit distribution is mixed normal. For d > 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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Publisher Info
Paper provided by Cowles Foundation, 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

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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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Find related papers by JEL classification:
C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions

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. 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. [Downloadable!] (restricted)
    Other versions:
  2. Donald W.K. Andrews & Yixiao Sun, 2001. "Local Polynomial Whittle Estimation of Long-range Dependence," Cowles Foundation Discussion Papers 1293, Cowles Foundation, Yale University. [Downloadable!]
  3. Katsumi Shimotsu & Peter C.B. Phillips, 2002. "Exact Local Whittle Estimation of Fractional Integration," Economics Discussion Papers 535, University of Essex, Department of Economics. [Downloadable!]
    Other versions:
  4. 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. [Downloadable!]
  5. Chang Sik Kim & Peter C.B. Phillips, 2006. "Log Periodogram Regression: The Nonstationary Case," Cowles Foundation Discussion Papers 1587, Cowles Foundation, Yale University. [Downloadable!]
  6. Schotman, Peter C & van Dijk, Herman K, 1991. "On Bayesian Routes to Unit Roots," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 6(4), pages 387-401, Oct.-Dec.. [Downloadable!] (restricted)
    Other versions:
  7. Peter C.B. Phillips, 1999. "Unit Root Log Periodogram Regression," Cowles Foundation Discussion Papers 1244, Cowles Foundation, Yale University. [Downloadable!]
    Other versions:
  8. Peter C.B. Phillips, 1999. "Discrete Fourier Transforms of Fractional Processes," Cowles Foundation Discussion Papers 1243, Cowles Foundation, Yale University. [Downloadable!]
Full references

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. Peter C.B. Phillips, 2004. "Challenges of Trending Time Series Econometrics," Cowles Foundation Discussion Papers 1472, Cowles Foundation, Yale University. [Downloadable!]
  2. Katsumi Shimotsu & Peter C.B. Phillips, 2002. "Exact Local Whittle Estimation of Fractional Integration," Economics Discussion Papers 535, University of Essex, Department of Economics. [Downloadable!]
    Other versions:
  3. Christian Fischer & Luis Alberiko Gil-Alana, 2005. "The Nature of the Relationship between International Tourism and International Trade: The Case of German Imports of Spanish Wine," Faculty Working Papers 15/05, School of Economics and Business Administration, University of Navarra. [Downloadable!]
    Other versions:
  4. Katsumi Shimotsu, 2003. "Exact Local Whittle Estimation of Fractionally Cointegrated Systems," Economics Discussion Papers 570, University of Essex, Department of Economics. [Downloadable!]
  5. Morten Ørregaard Nielsen & Per Frederiksen, 2005. "Finite Sample Comparison of Parametric, Semiparametric, and Wavelet Estimators of Fractional Integration," Working Papers 1189, Queen's University, Department of Economics. [Downloadable!]
  6. Katsumi Shimotsu, 2006. "Exact Local Whittle Estimation of Fractional Integration with Unknown Mean and Time Trend," Working Papers 1061, Queen's University, Department of Economics. [Downloadable!]
    Other versions:
  7. Katsumi Shimotsu, 2006. "Simple (but effective) tests of long memory versus structural breaks," Working Papers 1101, Queen's University, Department of Economics. [Downloadable!]
  8. Chang Sik Kim & Peter C.B. Phillips, 2006. "Log Periodogram Regression: The Nonstationary Case," Cowles Foundation Discussion Papers 1587, Cowles Foundation, Yale University. [Downloadable!]
  9. Wolfgang Härdle & Julius Mungo, 2008. "Value-at-Risk and Expected Shortfall when there is long range dependence," SFB 649 Discussion Papers SFB649DP2008-006, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany. [Downloadable!]
  10. Patrik Guggenberger & Yixiao Sun, 2004. "Bias-Reduced Log-Periodogram and Whittle Estimation of the Long-Memory Parameter Without Variance Inflation," University of California at San Diego, Economics Working Paper Series 2004-14, Department of Economics, UC San Diego. [Downloadable!]
  11. Henryk GURGUL & Tomasz WÓJTOWICZ, 2006. "Long Memory on the German Stock Exchange," Czech Journal of Economics and Finance (Finance a uver), Charles University Prague, Faculty of Social Sciences, vol. 56(09-10), pages 447-468, September. [Downloadable!]
  12. T. Di Matteo & T. Aste & Michel M. Dacorogna, 2005. "Long-term memories of developed and emerging markets: Using the scaling analysis to characterize their stage of development," Econometrics 0503004, EconWPA. [Downloadable!]
    Other versions:
  13. Katsumi Shimotsu, 2006. "Gaussian Semiparametric Estimation of Multivariate Fractionally Integrated Processes," Working Papers 1062, Queen's University, Department of Economics. [Downloadable!]
    Other versions:
  14. Haldrup, Niels & Nielsen, Morten Oe., . "Estimation of Fractional Integration in the Presence of Data Noise," Economics Working Papers 2003-10, School of Economics and Management, University of Aarhus. [Downloadable!]
    Other versions:
  15. Ling Hu & Peter C.B. Phillips, 2002. "Dynamics of the Federal Funds Target Rate: A Nonstationary Discrete Choice Approach," Cowles Foundation Discussion Papers 1365, Cowles Foundation, Yale University. [Downloadable!]
  16. Peter M Robinson, 2007. "Multiple Local Whittle Estimation in StationarySystems," STICERD - Econometrics Paper Series /2007/525, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE. [Downloadable!]
  17. Mohamed Boutahar & Gilles Dufrénot & Anne Péguin-Feissolle, 2008. "A Simple Fractionally Integrated Model with a Time-varying Long Memory Parameter d t ," Computational Economics, Springer, vol. 31(3), pages 225-241, April. [Downloadable!] (restricted)
  18. repec:bep:sndecm:11:2007:2:1382-1382 is not listed on IDEAS
  19. Frank S. Nielsen, 2008. "Local polynomial Whittle estimation covering non-stationary fractional processes," CREATES Research Papers 2008-28, School of Economics and Management, University of Aarhus. [Downloadable!]
  20. Wolfgang Härdle & Julius Mungo, 2007. "Long Memory Persistence in the Factor of Implied Volatility Dynamics," SFB 649 Discussion Papers SFB649DP2007-027, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany. [Downloadable!]
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This page was last updated on 2009-11-12.


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