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Unit Root Log Periodogram Regression

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

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Abstract

Log periodogram (LP) regression is shown to be consistent and to have a mixed normal limit distribution when the memory parameter d = 1. Gaussian errors are not required. Tests of d = 1 based on LP regression are consistent against d < 1 alternatives but inconsistent against d > 1 alternatives. A test based on a modified LP regression that is consistent in both directions is provided.

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File URL: http://cowles.econ.yale.edu/P/cd/d12a/d1244.pdf
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Publisher Info
Paper provided by Cowles Foundation, Yale University in its series Cowles Foundation Discussion Papers with number 1244.

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Length: 22 pages
Date of creation: Dec 1999
Date of revision:
Publication status: Published in Journal of Econometrics (2007), 138(1): 104-124
Handle: RePEc:cwl:cwldpp:1244

Note: CFP 1197.
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Postal: Yale University, Box 208281, New Haven, CT 06520-8281 USA
Phone: (203) 432-3702
Fax: (203) 432-6167
Web page: http://cowles.econ.yale.edu/
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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; log periodogram regression; long memory parameter; nonstationarity; semiparametric estimation and testing; 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. Peter C.B. Phillips & Victor Solo, 1989. "Asymptotics for Linear Processes," Cowles Foundation Discussion Papers 932, Cowles Foundation, Yale University. [Downloadable!]
  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. [Downloadable!] (restricted)
    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. Gil-Alana, L. A. & Robinson, P. M., 1997. "Testing of unit root and other nonstationary hypotheses in macroeconomic time series," Journal of Econometrics, Elsevier, vol. 80(2), pages 241-268, October. [Downloadable!] (restricted)
  5. Tanaka, Katsuto, 1999. "The Nonstationary Fractional Unit Root," Econometric Theory, Cambridge University Press, vol. 15(04), pages 549-582, August. [Downloadable!]
  6. Chang Sik Kim & Peter C.B. Phillips, 2006. "Log Periodogram Regression: The Nonstationary Case," Cowles Foundation Discussion Papers 1587, Cowles Foundation, Yale University. [Downloadable!]
  7. Schmidt, Peter & Phillips, C B Peter, 1992. "LM Tests for a Unit Root in the Presence of Deterministic Trends," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 54(3), pages 257-87, August.
  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. Jin Lee, 2004. "Wavelet transform for log periodogram regression in long memory stochastic volatility model," Econometric Society 2004 Far Eastern Meetings 682, Econometric Society. [Downloadable!]
  2. Peter C.B. Phillips & Binbin Guo & Zhijie Xiao, 2002. "Efficient Regression in Time Series Partial Linear Models," Cowles Foundation Discussion Papers 1363, Cowles Foundation, Yale University. [Downloadable!]
  3. Gary Biglaiser & Ching-to Albert Ma, 2006. "Moonlighting: Public Service and Private Practice," Boston University - Department of Economics - Working Papers Series WP2006-015, Boston University - Department of Economics. [Downloadable!]
    Other versions:
  4. Peter C.B. Phillips, 1999. "Discrete Fourier Transforms of Fractional Processes," Cowles Foundation Discussion Papers 1243, Cowles Foundation, Yale University. [Downloadable!]
  5. Pierre Perron & Zhongjun Qu, 2006. "An Analytical Evaluation of the Log-periodogram Estimate in the Presence of Level Shifts and its Implications for Stock Returns Volatility," Boston University - Department of Economics - Working Papers Series WP2006-016, Boston University - Department of Economics. [Downloadable!]
  6. Peter C.B. Phillips & Tassos Magadalinos, 2005. "Limit Theory for Moderate Deviations from a Unit Root under Weak Dependence," Cowles Foundation Discussion Papers 1517, Cowles Foundation, Yale University. [Downloadable!]
  7. Chang Sik Kim & Peter C.B. Phillips, 2006. "Log Periodogram Regression: The Nonstationary Case," Cowles Foundation Discussion Papers 1587, Cowles Foundation, Yale University. [Downloadable!]
  8. 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!]
  9. 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:
  10. Peter C. B. Phillips, 2006. "Optimal Estimation of Cointegrated Systems with Irrelevant Instruments," Cowles Foundation Discussion Papers 1547, Cowles Foundation, Yale University. [Downloadable!]
  11. Peter C.B. Phillips, 2004. "HAC Estimation by Automated Regression," Cowles Foundation Discussion Papers 1470, Cowles Foundation, Yale University. [Downloadable!]
    Other versions:
  12. Pierre Perron & Zhongjun Qu, 2007. "An Analytical Evaluation of the Log-periodogram Estimate in the Presence of Level Shifts," Boston University - Department of Economics - Working Papers Series wp2007-044, Boston University - Department of Economics. [Downloadable!]
  13. Katsumi Shimotsu, 2002. "Exact Local Whittle Estimation of Fractional Integration with Unknown Mean and Time Trend," Economics Discussion Papers 543, University of Essex, Department of Economics. [Downloadable!]
    Other versions:
  14. Basma Bekdache & Christopher F. Baum, 1999. "A re-evaluation of empirical tests of the Fisher hypothesis," Computing in Economics and Finance 1999 944, Society for Computational Economics, revised 18 Sep 2000. [Downloadable!]
    Other versions:
  15. Rustam Ibragimov & Peter C.B. Phillips, 2004. "Regression Asymptotics Using Martingale Convergence Methods," Cowles Foundation Discussion Papers 1473, Cowles Foundation, Yale University. [Downloadable!]
    Other versions:
  16. Christopher F. Baum & Mustafa Caglayan, 2008. "The Volatility of International Trade Flows and Exchange Rate Uncertainty," Boston College Working Papers in Economics 695, Boston College Department of Economics. [Downloadable!]
  17. Peter C.B. Phillips, 2001. "Bootstrapping Spurious Regression," Cowles Foundation Discussion Papers 1330, Cowles Foundation, Yale University. [Downloadable!]
  18. 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!]
  19. 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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This page was last updated on 2009-11-9.

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