IDEAS home Printed from https://ideas.repec.org/p/qed/wpaper/1061.html
   My bibliography  Save this paper

Exact Local Whittle Estimation of Fractional Integration with Unknown Mean and Time Trend

Author

Listed:
  • Katsumi Shimotsu

    () (Queen's University)

Abstract

Recently, Shimotsu and Phillips (2005) developed a new semiparametric estimator, the exact local Whittle (ELW) estimator, of the memory parameter (d) in fractionally integrated processes. The ELW estimator has been shown to be consistent and have the same N(0,1/4) limit distribution for all values of d if the optimization covers an interval of width less than 9/2 and the mean of the process is known. With the intent to provide an efficient semiparametric estimator suitable for economic data, we extend the ELW estimator so that it accommodates an unknown mean and a polynomial time trend. We show that the resulting feasible ELW estimator is consistent and has a N(0,1/4) limit distribution for -1/2

Suggested Citation

  • Katsumi Shimotsu, 2006. "Exact Local Whittle Estimation of Fractional Integration with Unknown Mean and Time Trend," Working Paper 1061, Economics Department, Queen's University.
  • Handle: RePEc:qed:wpaper:1061
    as

    Download full text from publisher

    File URL: http://qed.econ.queensu.ca/working_papers/papers/qed_wp_1061.pdf
    File Function: First version 2006
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Diebold, Francis X & Rudebusch, Glenn D, 1991. "Is Consumption Too Smooth? Long Memory and the Deaton Paradox," The Review of Economics and Statistics, MIT Press, vol. 73(1), pages 1-9, February.
    2. Hassler, Uwe & Wolters, Jurgen, 1995. "Long Memory in Inflation Rates: International Evidence," Journal of Business & Economic Statistics, American Statistical Association, vol. 13(1), pages 37-45, January.
    3. Kwiatkowski, Denis & Phillips, Peter C. B. & Schmidt, Peter & Shin, Yongcheol, 1992. "Testing the null hypothesis of stationarity against the alternative of a unit root : How sure are we that economic time series have a unit root?," Journal of Econometrics, Elsevier, vol. 54(1-3), pages 159-178.
    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.
    5. Lobato, Ignacio N., 1999. "A semiparametric two-step estimator in a multivariate long memory model," Journal of Econometrics, Elsevier, vol. 90(1), pages 129-153, May.
    6. Robinson, Peter M, 1988. "The Stochastic Difference between Econometric Statistics," Econometrica, Econometric Society, vol. 56(3), pages 531-548, May.
    7. Crato, Nuno & Rothman, Philip, 1994. "Fractional integration analysis of long-run behavior for US macroeconomic time series," Economics Letters, Elsevier, vol. 45(3), pages 287-291.
    8. Michelacci, Claudio & Zaffaroni, Paolo, 2000. "(Fractional) beta convergence," Journal of Monetary Economics, Elsevier, vol. 45(1), pages 129-153, February.
    9. Haubrich, Joseph G, 1993. "Consumption and Fractional Differencing: Old and New Anomalies," The Review of Economics and Statistics, MIT Press, vol. 75(4), pages 767-772, November.
    10. 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.
    11. 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..
    12. Robinson, P.M., 2005. "The distance between rival nonstationary fractional processes," Journal of Econometrics, Elsevier, vol. 128(2), pages 283-300, October.
    13. David K. Backus & Stanley E. Zin, 1993. "Long-memory inflation uncertainty: evidence from the term structure of interest rates," Proceedings, Federal Reserve Bank of Cleveland, pages 681-708.
    14. Lobato, Ignacio N & Velasco, Carlos, 2000. "Long Memory in Stock-Market Trading Volume," Journal of Business & Economic Statistics, American Statistical Association, vol. 18(4), pages 410-427, October.
    15. 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.
    16. 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.
    17. Nelson, Charles R. & Plosser, Charles I., 1982. "Trends and random walks in macroeconmic time series : Some evidence and implications," Journal of Monetary Economics, Elsevier, vol. 10(2), pages 139-162.
    18. 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.
    19. Carlos Velasco, 2003. "Gaussian Semi‐parametric Estimation of Fractional Cointegration," Journal of Time Series Analysis, Wiley Blackwell, vol. 24(3), pages 345-378, May.
    Full references (including those not matched with items on IDEAS)

    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. Shimotsu, Katsumi, 2002. "Exact Local Whittle Estimation of Fractional Integration with Unknown Mean and Time Trend," Economics Discussion Papers 8844, University of Essex, Department of Economics.
    2. Baillie, Richard T., 1996. "Long memory processes and fractional integration in econometrics," Journal of Econometrics, Elsevier, vol. 73(1), pages 5-59, July.
    3. Guglielmo Maria Caporale & Luis Gil‐Alana, 2014. "Long‐Run and Cyclical Dynamics in the US Stock Market," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 33(2), pages 147-161, March.
    4. Arteche, Josu & Orbe, Jesus, 2009. "Using the bootstrap for finite sample confidence intervals of the log periodogram regression," Computational Statistics & Data Analysis, Elsevier, vol. 53(6), pages 1940-1953, April.
    5. Shimotsu, Katsumi, 2012. "Exact local Whittle estimation of fractionally cointegrated systems," Journal of Econometrics, Elsevier, vol. 169(2), pages 266-278.
    6. Guglielmo Caporale & Luis Gil-Alana, 2013. "Long memory in US real output per capita," Empirical Economics, Springer, vol. 44(2), pages 591-611, April.
    7. Cuestas, Juan C. & Gil-Alana, Luís A., 2009. "Further evidence on the PPP analysis of the Australian dollar: Non-linearities, fractional integration and structural changes," Economic Modelling, Elsevier, vol. 26(6), pages 1184-1192, November.
    8. Morten Ørregaard Nielsen & Per Houmann Frederiksen, 2005. "Finite Sample Comparison of Parametric, Semiparametric, and Wavelet Estimators of Fractional Integration," Econometric Reviews, Taylor & Francis Journals, vol. 24(4), pages 405-443.
    9. Haldrup, Niels & Nielsen, Morten Orregaard, 2007. "Estimation of fractional integration in the presence of data noise," Computational Statistics & Data Analysis, Elsevier, vol. 51(6), pages 3100-3114, March.
    10. Giorgio Canarella & Stephen Miller, 2016. "Inflation persistence and structural breaks: the experience of inflation targeting countries and the US," Journal of Economic Studies, Emerald Group Publishing, vol. 43(6), pages 980-1005, November.
    11. Giorgio Canarella & Stephen M. Miller, 2016. "Inflation Targeting: New Evidence from Fractional Integration and Cointegration," Working papers 2016-08, University of Connecticut, Department of Economics.
    12. John Barkoulas & Christopher Baum & Mustafa Caglayan, 1999. "Fractional monetary dynamics," Applied Economics, Taylor & Francis Journals, vol. 31(11), pages 1393-1400.
    13. Nielsen, Morten Orregaard & Shimotsu, Katsumi, 2007. "Determining the cointegrating rank in nonstationary fractional systems by the exact local Whittle approach," Journal of Econometrics, Elsevier, vol. 141(2), pages 574-596, December.
    14. Luis Gil-Alana, 2003. "Strong dependence in the real interest rates," Applied Economics, Taylor & Francis Journals, vol. 35(2), pages 119-124.
    15. Christian Fischer & Luis Alberiko Gil-Alana, 2005. "The Nature of the Relationship between International Tourism and International Trade: The Case of Ge," Faculty Working Papers 15/05, School of Economics and Business Administration, University of Navarra.
    16. Frank S. Nielsen, 2009. "Local Whittle estimation of multivariate fractionally integrated processes," CREATES Research Papers 2009-38, Department of Economics and Business Economics, Aarhus University.
    17. Carlos Barros & Luis Gil-Alana, 2013. "Inflation Forecasting in Angola: A Fractional Approach," African Development Review, African Development Bank, vol. 25(1), pages 91-104.
    18. 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.
    19. Katsumi Shimotsu, 2006. "Simple (but Effective) Tests Of Long Memory Versus Structural Breaks," Working Paper 1101, Economics Department, Queen's University.
    20. 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.

    More about this item

    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:qed:wpaper:1061. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Mark Babcock). General contact details of provider: https://edirc.repec.org/data/qedquca.html .

    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 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.

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.