Jensen, Mark J (1999): Using wavelets to obtain a consistent ordinary least squares estimator of the longmemory parameter. Published in: Journal of Forecasting , Vol. 18, (1999): pp. 1732.

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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 PorterHudak estimator. Using the wavelet transform from a fractionally integrated process, we establish a loglinear relationship between the wavelet coefficients' variance and the scaling parameter equal to the long memory parameter. This loglinear 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 PorterHudak 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 PorterHudak 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.
Item Type:  MPRA Paper 

Original Title:  Using wavelets to obtain a consistent ordinary least squares estimator of the longmemory parameter 
Language:  English 
Keywords:  Fractionally Integrated Processes; Long Memory; Wavelets 
Subjects:  C  Mathematical and Quantitative Methods > C2  Single Equation Models ; Single Variables > C22  TimeSeries Models ; Dynamic Quantile Regressions ; Dynamic Treatment Effect Models ; Diffusion Processes 
Item ID:  39152 
Depositing User:  Mark Jensen 
Date Deposited:  31 May 2012 12:54 
Last Modified:  24 Jul 2016 23:27 
References:  Mark J. Jensen, 1997. "Using Wavelets to Obtain a Consistent Ordinary Least Squares Estimator of the Long Memory Parameter," Econometrics 9710002, EconWPA. Mark J. Jensen, 1995. "OLS Estimate of Fractional Differencing Parameter Using Wavelets Derived from Smoothing Kernels," Econometrics 9506002, EconWPA. 
URI:  https://mpra.ub.unimuenchen.de/id/eprint/39152 