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Log Periodogram Regression: The Nonstationary Case

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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 1, the estimator is shown to converge in probability to unity.

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  • 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.
    • Handle: RePEc:cwl:cwldpp:1587
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    File URL: https://cowles.yale.edu/sites/default/files/files/pub/d15/d1587.pdf
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    References listed on IDEAS

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    1. Peter C.B. Phillips, 1999. "Discrete Fourier Transforms of Fractional Processes," Cowles Foundation Discussion Papers 1243, Cowles Foundation for Research in Economics, Yale University.
    2. Velasco, Carlos, 2000. "Non-Gaussian Log-Periodogram Regression," Econometric Theory, Cambridge University Press, vol. 16(1), pages 44-79, February.
    3. Clifford M. Hurvich & Bonnie K. Ray, 1995. "Estimation Of The Memory Parameter For Nonstationary Or Noninvertible Fractionally Integrated Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 16(1), pages 17-41, January.
    4. Velasco, Carlos, 1999. "Non-stationary log-periodogram regression," Journal of Econometrics, Elsevier, vol. 91(2), pages 325-371, August.
    5. Clifford M. Hurvich & Rohit Deo & Julia Brodsky, 1998. "The mean squared error of Geweke and Porter‐Hudak's estimator of the memory parameter of a long‐memory time series," Journal of Time Series Analysis, Wiley Blackwell, vol. 19(1), pages 19-46, January.
    6. 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.
    7. Peter C.B. Phillips & Victor Solo, 1989. "Asymptotics for Linear Processes," Cowles Foundation Discussion Papers 932, Cowles Foundation for Research in Economics, Yale University.
    8. Phillips, Peter C.B., 2007. "Unit root log periodogram regression," Journal of Econometrics, Elsevier, vol. 138(1), pages 104-124, May.
    9. Chen Zhao‐Guo & E. J. Hannan, 1980. "The Distribution Of Periodogram Ordinates," Journal of Time Series Analysis, Wiley Blackwell, vol. 1(1), pages 73-82, January.
    10. Christos Agiakloglou & Paul Newbold & Mark Wohar, 1993. "Bias In An Estimator Of The Fractional Difference Parameter," Journal of Time Series Analysis, Wiley Blackwell, vol. 14(3), pages 235-246, May.
    11. Abadir, Karim M. & Distaso, Walter & Giraitis, Liudas, 2007. "Nonstationarity-extended local Whittle estimation," Journal of Econometrics, Elsevier, vol. 141(2), pages 1353-1384, December.
    12. Liu, Ming, 1998. "Asymptotics Of Nonstationary Fractional Integrated Series," Econometric Theory, Cambridge University Press, vol. 14(5), pages 641-662, October.
    13. 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.
    14. 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 103-112, January.
    15. Katsumi Shimotsu & Peter C.B. Phillips, 2000. "Local Whittle Estimation in Nonstationary and Unit Root Cases," Cowles Foundation Discussion Papers 1266, Cowles Foundation for Research in Economics, Yale University, revised Sep 2003.
    16. Carlos Velasco, 2003. "Gaussian Semi‐parametric Estimation of Fractional Cointegration," Journal of Time Series Analysis, Wiley Blackwell, vol. 24(3), pages 345-378, May.
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    More about this item

    Keywords

    Discrete Fourier transform; Fractional Brownian motion; Fractional integration; Inconsistency; Log periodogram regression; Long memory parameter; Nonstationarity; Semiparametric estimation;
    All these keywords.

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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