IDEAS home Printed from https://ideas.repec.org/p/cwl/cwldpp/1265.html
   My bibliography  Save this paper

Modified Local Whittle Estimation of the Memory Parameter in the Nonstationary Case

Author

Abstract

Semiparametric estimation of the memory parameter is studied in models of fractional integration in the nonstationary case, and some new representation theory for the discrete Fourier transform of a fractional process is used to assist in the analysis. A limit theory is developed for an estimator of the memory parameter that covers a range of values of d commonly encountered in applied work with economic data. The new estimator is called the modified local Whittle estimator and employs a version of the Whittle likelihood based on frequencies adjacent to the origin and modified to take into account the form of the data generating mechanism in the frequency domain. The modified local Whittle estimator is shown to be consistent for 0

Suggested Citation

  • Katsumi Shimotsu & Peter C.B. Phillips, 2000. "Modified Local Whittle Estimation of the Memory Parameter in the Nonstationary Case," Cowles Foundation Discussion Papers 1265, Cowles Foundation for Research in Economics, Yale University.
    • Handle: RePEc:cwl:cwldpp:1265
    as

    Download full text from publisher

    File URL: https://cowles.yale.edu/sites/default/files/files/pub/d12/d1265.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    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, 1999. "Non-stationary log-periodogram regression," Journal of Econometrics, Elsevier, vol. 91(2), pages 325-371, August.
    3. Peter C.B. Phillips & Victor Solo, 1989. "Asymptotics for Linear Processes," Cowles Foundation Discussion Papers 932, Cowles Foundation for Research in Economics, Yale University.
    4. Velasco, Carlos, 1998. "Non-stationary log-periodogram regression," DES - Working Papers. Statistics and Econometrics. WS 4554, Universidad Carlos III de Madrid. Departamento de Estadística.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Arielle Beyaert, 2004. "Fractional Output Convergence, with an Application to Nine Developed Countries," Econometric Society 2004 Australasian Meetings 280, Econometric Society.
    2. John W. Galbraith & Victoria Zinde-Walsh, 2001. "Autoregression-Based Estimators for ARFIMA Models," CIRANO Working Papers 2001s-11, CIRANO.
    3. Gilles Dufrénot & Valérie Mignon & Théo Naccache, 2009. "The slow convergence of per capita income between the developing countries: “growth resistance” and sometimes “growth tragedy”," Discussion Papers 09/03, University of Nottingham, CREDIT.
    4. Dominique Guegan & Zhiping Lu & Beijia Zhu, 2012. "Comparaison of Several Estimation Procedures for Long Term Behavior," Post-Print halshs-00673934, HAL.
    5. Han, Young Wook, 2005. "Long memory volatility dependency, temporal aggregation and the Korean currency crisis: the role of a high frequency Korean won (KRW)-US dollar ($) exchange rate," Japan and the World Economy, Elsevier, vol. 17(1), pages 97-109, January.
    6. Dominique Guegan & Zhiping Lu & Beijia Zhu, 2012. "Comparaison of Several Estimation Procedures for Long Term Behavior," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00673934, HAL.
    7. Shimotsu, Katsumi & Phillips, Peter C.B., 2006. "Local Whittle estimation of fractional integration and some of its variants," Journal of Econometrics, Elsevier, vol. 130(2), pages 209-233, February.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. Phillips, Peter C.B., 2007. "Unit root log periodogram regression," Journal of Econometrics, Elsevier, vol. 138(1), pages 104-124, May.
    3. Ulrich K. Müller & Mark W. Watson, 2008. "Testing Models of Low-Frequency Variability," Econometrica, Econometric Society, vol. 76(5), pages 979-1016, September.
    4. Georgios P. Kouretas & Mark E. Wohar, 2012. "The dynamics of inflation: a study of a large number of countries," Applied Economics, Taylor & Francis Journals, vol. 44(16), pages 2001-2026, June.
    5. Shimotsu, Katsumi & Phillips, Peter C.B., 2006. "Local Whittle estimation of fractional integration and some of its variants," Journal of Econometrics, Elsevier, vol. 130(2), pages 209-233, February.
    6. João Valle e Azevedo, 2007. "Exact Limit of the Expected Periodogram in the Unit-Root case," Working Papers w200713, Banco de Portugal, Economics and Research Department.
    7. Luis A. Gil-Alana & Antonio Moreno & Seonghoon Cho, 2012. "The Deaton paradox in a long memory context with structural breaks," Applied Economics, Taylor & Francis Journals, vol. 44(25), pages 3309-3322, September.
    8. Miguel A. Delgado & Javier Hidalgo & Carlos Velasco, 2005. "Distribution Free Goodness-of-Fit Tests for Linear Processes," STICERD - Econometrics Paper Series 482, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    9. Philipp Sibbertsen, 2004. "Long memory versus structural breaks: An overview," Statistical Papers, Springer, vol. 45(4), pages 465-515, October.
    10. Arteche, J., 2006. "Semiparametric estimation in perturbed long memory series," Computational Statistics & Data Analysis, Elsevier, vol. 51(4), pages 2118-2141, December.
    11. Javier Hualde & Morten Ørregaard Nielsen, 2022. "Truncated sum-of-squares estimation of fractional time series models with generalized power law trend," CREATES Research Papers 2022-07, Department of Economics and Business Economics, Aarhus University.
    12. Adam McCloskey, 2013. "Estimation of the long-memory stochastic volatility model parameters that is robust to level shifts and deterministic trends," Journal of Time Series Analysis, Wiley Blackwell, vol. 34(3), pages 285-301, May.
    13. Mccloskey, Adam & Perron, Pierre, 2013. "Memory Parameter Estimation In The Presence Of Level Shifts And Deterministic Trends," Econometric Theory, Cambridge University Press, vol. 29(6), pages 1196-1237, December.
    14. Yaya, OlaOluwa S. & Vo, Xuan Vinh & Olayinka, Hammed A., 2021. "Gold and silver prices, their stocks and market fear gauges: Testing fractional cointegration using a robust approach," Resources Policy, Elsevier, vol. 72(C).
    15. Liudas Giraitis & Peter M Robinson, 2002. "Edgeworth Expansions for Semiparametric Whittle Estimation of Long Memory," STICERD - Econometrics Paper Series 438, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    16. Dolado, Juan José & Gonzalo, Jesús & Mayoral, Laura, 2008. "Simple Wald tests of the fractional integration parameter : an overview of new results," UC3M Working papers. Economics we20080129, Universidad Carlos III de Madrid. Departamento de Economía.
    17. Giraitis, L. & Robinson, P.M., 2003. "Edgeworth expansions for semiparametric Whittle estimation of long memory," LSE Research Online Documents on Economics 291, London School of Economics and Political Science, LSE Library.
    18. Guglielmo Caporale & Luis Gil-Alana, 2013. "Long memory in US real output per capita," Empirical Economics, Springer, vol. 44(2), pages 591-611, April.
    19. de Truchis, Gilles, 2013. "Approximate Whittle analysis of fractional cointegration and the stock market synchronization issue," Economic Modelling, Elsevier, vol. 34(C), pages 98-105.
    20. Peter C. B. Phillips, 2023. "Discrete Fourier Transforms of Fractional Processes with Econometric Applications," Advances in Econometrics, in: Essays in Honor of Joon Y. Park: Econometric Theory, volume 45, pages 3-71, Emerald Group Publishing Limited.

    More about this item

    Keywords

    Discrete Fourier transform; fractional Brownian motion; fractional integration; long memory; nonstationarity; semiparametric estimation; Whittle likelihood;
    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

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:cwl:cwldpp:1265. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Brittany Ladd (email available below). General contact details of provider: https://edirc.repec.org/data/cowleus.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.