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Log Periodogram Regression: The Nonstationary Case

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Author Info
Chang Sik Kim (Dept. of Economics, Ewha Women's University)
Peter C.B. Phillips () (Cowles Foundation, Yale University)

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Abstract

Estimation of the memory parameter (d) is considered for models of nonstationary fractionally integrated time series with d > (1/2). It is shown that the log periodogram regression estimator of d is inconsistent when 1 < d < 2 and is consistent when (1/2) < d = 1. For d > 1, the estimator is shown to converge in probability to unity.

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File URL: http://cowles.econ.yale.edu/P/cd/d15b/d1587.pdf
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Publisher Info
Paper provided by Cowles Foundation, Yale University in its series Cowles Foundation Discussion Papers with number 1587.

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Length: 29 pages
Date of creation: Oct 2006
Date of revision:
Handle: RePEc:cwl:cwldpp:1587

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Related research
Keywords: Discrete Fourier transform; Fractional Brownian motion; Fractional integration; Inconsistency; Log periodogram regression; Long memory parameter; Nonstationarity; Semiparametric estimation;

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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

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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. Peter C.B. Phillips & Victor Solo, 1989. "Asymptotics for Linear Processes," Cowles Foundation Discussion Papers 932, Cowles Foundation, Yale University. [Downloadable!]
  2. Velasco, Carlos, 1999. "Non-stationary log-periodogram regression," Journal of Econometrics, Elsevier, vol. 91(2), pages 325-371, August. [Downloadable!] (restricted)
  3. Abadir, Karim M. & Distaso, Walter & Giraitis, Liudas, 2007. "Nonstationarity-extended local Whittle estimation," Journal of Econometrics, Elsevier, vol. 141(2), pages 1353-1384, December. [Downloadable!] (restricted)
  4. Liu, Ming, 1998. "Asymptotics Of Nonstationary Fractional Integrated Series," Econometric Theory, Cambridge University Press, vol. 14(05), pages 641-662, October. [Downloadable!]
  5. Cheung, Yin-Wong & Lai, Kon S, 1993. "A Fractional Cointegration Analysis of Purchasing Power Parity," Journal of Business & Economic Statistics, American Statistical Association, vol. 11(1), pages 103-12, January.
  6. Katsumi Shimotsu & Peter C.B. Phillips, 2000. "Local Whittle Estimation in Nonstationary and Unit Root Cases," Cowles Foundation Discussion Papers 1266, Cowles Foundation, Yale University, revised Sep 2003. [Downloadable!]
  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!]
  9. Alex Maynard & Peter C. B. Phillips, 2001. "Rethinking an old empirical puzzle: econometric evidence on the forward discount anomaly," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 16(6), pages 671-708. [Downloadable!]
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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. 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:
  2. 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:
  3. 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!]
  4. 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!]
  5. 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!]
  6. Basma Bekdache & Christopher F. Baum, 2000. "A re-evaluation of empirical tests of the Fisher hypothesis," Boston College Working Papers in Economics 472, Boston College Department of Economics. [Downloadable!]
    Other versions:
  7. Katsumi Shimotsu & Peter C.B. Phillips, 2000. "Local Whittle Estimation in Nonstationary and Unit Root Cases," Cowles Foundation Discussion Papers 1266, Cowles Foundation, Yale University, revised Sep 2003. [Downloadable!]
  8. Peter C.B. Phillips, 1999. "Unit Root Log Periodogram Regression," Cowles Foundation Discussion Papers 1244, Cowles Foundation, Yale University. [Downloadable!]
    Other versions:
  9. Michael Kühl, 2008. "Strong comovements of exchange rates: Theoretical and empirical cases when currencies become the same asset," cege – Center for European, Governance and Economic Development Research Discussion Papers 76, cege – Center for European, Governance and Economic Development Research, University of Goettingen (Germany)., revised 03 Sep 2008. [Downloadable!]
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