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Using Wavelets to Obtain a Consistent Ordinary Least Squares Estimator of the Long Memory Parameter

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Author Info
Mark J. Jensen (University of Missouri - Columbia)

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Abstract

We develop an ordinary least squares estimator of the long memory parameter from a fractionally integrated process that is an alternative to the Geweke Porter-Hudak estimator. Using the wavelet transform from a fractionally integrated process, we establish a log-linear relationship between the wavelet coefficients' variance and the scaling parameter equal to the long memory parameter. This log-linear relationship yields a consistent ordinary least squares estimator of the long memory parameter when the wavelet coefficients' population varinace is replaced by their sample variance. We derive the small sample bias and variance of the ordinary least squares estimator and test it against the Geweke Porter-Hudak estimator and the McCoy Walden maximum likelihood wavelet estimator by conducting a number of Monte Carlo experiments. Based upon the criterion of choosing the estimator which minimizes the mean squared error, the wavelet OLS approach was superior to the Geweke Porter-Hudak estimator, but inferior to the McCoy Walden wavelet estimator for the processes simulated. However, given the simplicity of programming and running the wavelet OLS estimator and its statistical inference of the long memory parameter we feel the general practitioner will be attracted to the wavelet OLS estimator.

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Paper provided by EconWPA in its series Econometrics with number 9710002.

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Length: 22 pages
Date of creation: 31 Oct 1997
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Handle: RePEc:wpa:wuwpem:9710002

Note: Type of Document - TeX; prepared on Unix Ultra 100 Solaris 2.5; to print on PostScript; pages: 22 ; figures: included
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Related research
Keywords: Fractionally Integrated Processes; Long Memory; Wavelets;

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Find related papers by JEL classification:
C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Statistical Simulation Methods
C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions

References listed on IDEAS
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  1. 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.
    Other versions:
  2. 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)
    Other versions:
  3. 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.
  4. C. M. Schmidt & R. Tschernig, . "The Identification of Fractional ARIMA Models," Sonderforschungsbereich 373 1995-8, Humboldt Universitaet Berlin.
  5. Ding, Zhuanxin & Granger, Clive W. J. & Engle, Robert F., 1993. "A long memory property of stock market returns and a new model," Journal of Empirical Finance, Elsevier, vol. 1(1), pages 83-106, June. [Downloadable!] (restricted)
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  6. Baillie, Richard T & Bollerslev, Tim, 1994. " Cointegration, Fractional Cointegration, and Exchange Rate Dynamics," Journal of Finance, American Finance Association, vol. 49(2), pages 737-45, June. [Downloadable!] (restricted)
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  7. Cheung, Yin-Wong, 1993. "Long Memory in Foreign-Exchange Rates," Journal of Business & Economic Statistics, American Statistical Association, vol. 11(1), pages 93-101, January.
  8. Lo, Andrew W, 1991. "Long-Term Memory in Stock Market Prices," Econometrica, Econometric Society, vol. 59(5), pages 1279-313, September. [Downloadable!] (restricted)
    Other versions:
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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. Elder, John & Jin, Hyun J. & Koo, Won W., 2004. "A Reexamination Of Fractional Integrating Dynamics In Foreign Currency Markets," 2004 Annual meeting, August 1-4, Denver, CO 20004, American Agricultural Economics Association (New Name 2008: Agricultural and Applied Economics Association). [Downloadable!]
    Other versions:
  2. Christoph Schleicher, 2002. "An Introduction to Wavelets for Economists," Working Papers 02-3, Bank of Canada. [Downloadable!]
  3. Collet J.J. & Fadili J.M., 2005. "Simulation of Gegenbauer processes using wavelet packets," School of Economics and Finance Discussion Papers and Working Papers Series 190, School of Economics and Finance, Queensland University of Technology. [Downloadable!]
  4. 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!]
  5. Ramsey, J.B., 2002. "Wavelets in Economics and Finance: Past and Future," Working Papers 02-02, C.V. Starr Center for Applied Economics, New York University. [Downloadable!]
  6. Cotter, John & Dowd, Kevin, 2006. "U.S. Core Inflation: A Wavelet Analysis," MPRA Paper 3520, University Library of Munich, Germany. [Downloadable!]
  7. Patrick Crowley, 2005. "An intuitive guide to wavelets for economists," Econometrics 0503017, EconWPA. [Downloadable!]
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  8. Gilles Dufrénot & Valérie Mignon & Théo Naccache, . "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. [Downloadable!]
  9. Jennifer Brown & Les Oxley & William Rea & Marco Reale, 2008. "The Empirical Properties of Some Popular Estimators of Long Memory Processes," Working Papers in Economics 08/13, University of Canterbury, Department of Economics. [Downloadable!]
  10. Brandon Whitcher, 2000. "Wavelet-Based Estimation Procedures For Seasonal Long-Memory Models," Computing in Economics and Finance 2000 148, Society for Computational Economics. [Downloadable!]
  11. Derek Bond & Michael J. Harrison & Edward J. O'Brien, 2005. "Testing for Long Memory and Nonlinear Time Series: A Demand for Money Study," Trinity Economics Papers tep20021, Trinity College Dublin, Department of Economics. [Downloadable!]
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  12. Mark J. Jensen, 1999. "An Approximate Wavelet MLE of Short- and Long-Memory Parameters," Computing in Economics and Finance 1999 1243, Society for Computational Economics. [Downloadable!]
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  13. 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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