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

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Katsumi Shimotsu ()

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Abstract

Recently Shimotsu and Phillips (2002, Essex Discussion Paper 535) 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. With economic applications in mind, we extend the ELW estimator so that it accommodates an unknown mean and a linear time trend. We show the resulting feasible ELW estimator is consistent for d > -1/2 and has a N(0, 1/4 ) limit distribution for d in (-1/2, 2) (d in (-1/2, 7/4) when the data have a linear trend) except for a few negligible intervals. A simulation study shows that the feasible ELW estimator inherits the desirable properties of the ELW estimator also in small samples.

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Paper provided by University of Essex, Department of Economics in its series Economics Discussion Papers with number 543.

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Date of creation: 20 Aug 2002
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Handle: RePEc:esx:essedp:543

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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. Robinson, Peter M, 1988. "The Stochastic Difference between Econometric Statistics," Econometrica, Econometric Society, vol. 56(3), pages 531-48, May. [Downloadable!] (restricted)
  2. 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. [Downloadable!] (restricted)
  3. Michelacci, C. & Zaffaroni, P., 2000. "(Fractional) Beta Convergence," Papers 383, Banca Italia - Servizio di Studi.
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  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. 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!]
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  6. 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. [Downloadable!] (restricted)
  7. Joseph G. Haubrich, 1990. "Consumption and fractional differencing: old and new anomalies," Working Paper 9010, Federal Reserve Bank of Cleveland. [Downloadable!]
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  8. 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. [Downloadable!] (restricted)
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  9. Robinson, P.M., 2005. "The distance between rival nonstationary fractional processes," Journal of Econometrics, Elsevier, vol. 128(2), pages 283-300, October. [Downloadable!] (restricted)
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  10. 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.
  11. Chang Sik Kim & Peter C.B. Phillips, 2006. "Log Periodogram Regression: The Nonstationary Case," Cowles Foundation Discussion Papers 1587, Cowles Foundation, Yale University. [Downloadable!]
  12. 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. [Downloadable!] (restricted)
  13. 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 410-27, October.
  14. 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.. [Downloadable!] (restricted)
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  15. 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!]
  16. Peter C.B. Phillips, 1999. "Unit Root Log Periodogram Regression," Cowles Foundation Discussion Papers 1244, Cowles Foundation, Yale University. [Downloadable!]
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  17. Marc Henry & Paolo Zaffaroni, 2002. "The long range dependence paradigm for macroeconomics and finance," Discussion Papers 0102-19, Columbia University, Department of Economics. [Downloadable!]
  18. 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. [Downloadable!] (restricted)
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  19. Backus, David K & Zin, Stanley E, 1993. "Long-Memory Inflation Uncertainty: Evidence from the Term Structure of Interest Rates," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 25(3), pages 681-700, August. [Downloadable!] (restricted)
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  20. 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. Krüger, Niclas A, 2008. "Climate Variability and Health: Sweden 1751-2004," Working Papers 2008:4, Örebro University, Swedish Business School. [Downloadable!]
  2. Tatsuyoshi Okimoto & Katsumi Shimotsu, 2007. "Financial Market Integration and World Economic Stabilization toward Purchasing Power Parity," Working Papers 1138, Queen's University, Department of Economics. [Downloadable!]
  3. Morten Ørregaard Nielsen & Per Frederiksen, 2005. "Finite Sample Comparison of Parametric, Semiparametric, and Wavelet Estimators of Fractional Integration," Working Papers 1189, Queen's University, Department of Economics. [Downloadable!]
  4. Katsumi Shimotsu, 2006. "Simple (but effective) tests of long memory versus structural breaks," Working Papers 1101, Queen's University, Department of Economics. [Downloadable!]
  5. Gervais, Jean-Philippe, 2007. "Disentangling non-linearities in the long- and short-run price relationships: An application to the U.S. hog/Pork supply chain," MPRA Paper 7743, University Library of Munich, Germany, revised 15 Jan 2008. [Downloadable!]
  6. Morten Ørregaard Nielsen, 2008. "Nonparametric Cointegration Analysis of Fractional Systems With Unknown Integration Orders," Working Papers 1174, Queen's University, Department of Economics. [Downloadable!]
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  7. Bond, Derek & Dyson, Kenneth, 2006. "Long memory and non-linearity in Stock Markets," MPRA Paper 252, University Library of Munich, Germany. [Downloadable!]
    Other versions:
  8. Mohamed Boutahar & Gilles Dufrénot & Anne Péguin-Feissolle, 2008. "A Simple Fractionally Integrated Model with a Time-varying Long Memory Parameter d t ," Computational Economics, Springer, vol. 31(3), pages 225-241, April. [Downloadable!] (restricted)
  9. David Berger & Alain Chaboud & Erik Hjalmarsson & Edward Howorka, 2006. "What drives volatility persistence in the foreign exchange market?," International Finance Discussion Papers 862, Board of Governors of the Federal Reserve System (U.S.). [Downloadable!]
  10. Katsumi Shimotsu & Morten Ørregaard Nielsen, 2006. "Determining the Cointegrating Rank in Nonstationary Fractional Systems by the Exact Local Whittle Approach," Working Papers 1029, Queen's University, Department of Economics. [Downloadable!]
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  11. Frank S. Nielsen, 2008. "Local polynomial Whittle estimation covering non-stationary fractional processes," CREATES Research Papers 2008-28, School of Economics and Management, University of Aarhus. [Downloadable!]
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