Using Wavelets to Obtain a Consistent Ordinary Least Squares Estimator of the Long Memory Parameter
AbstractWe 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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Bibliographic InfoPaper provided by EconWPA in its series Econometrics with number 9710002.
Length: 22 pages
Date of creation: 31 Oct 1997
Date of revision:
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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Fractionally Integrated Processes; Long Memory; Wavelets;
Other versions of this item:
- Jensen, Mark J, 1999. "Using wavelets to obtain a consistent ordinary least squares estimator of the long-memory parameter," MPRA Paper 39152, University Library of Munich, Germany.
- C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
- C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models &bull Diffusion Processes
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