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

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.