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Using wavelets to obtain a consistent ordinary least squares estimator of the long-memory parameter

  • Jensen, Mark J

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 University Library of Munich, Germany in its series MPRA Paper with number 39152.

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Date of creation: 1999
Date of revision:
Handle: RePEc:pra:mprapa:39152
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  1. Baillie, R.T. & Bollerslev, T., 1993. "Cointegration, Fractional Cointegration, and Exchange RAte Dynamics," Papers 9103, Michigan State - Econometrics and Economic Theory.
  2. 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.
  3. Lo, Andrew W, 1991. "Long-Term Memory in Stock Market Prices," Econometrica, Econometric Society, vol. 59(5), pages 1279-313, September.
  4. David K. Backus, 1993. "Long-Memory Inflation Uncertainty: Evidence from the Term Structure of Interest Rates," Working Papers 93-04, New York University, Leonard N. Stern School of Business, Department of Economics.
  5. C. M. Schmidt & R. Tschernig, 1995. "The Identification of Fractional ARIMA Models," SFB 373 Discussion Papers 1995,8, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
  6. Francis X. Diebold & Glenn D. Rudebusch, 1989. "Is consumption too smooth? Long memory and the Deaton paradox," Finance and Economics Discussion Series 57, Board of Governors of the Federal Reserve System (U.S.).
  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. 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.
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