Maximum likelihood estimation of the fractional differencing parameter in an ARFIMA model using wavelets

In this paper we examine the ̄nite-sample properties of the approximate maximum likelihood estimate (MLE) of the fractional di®erencing parameter d in an ARFIMA(p, d, q) model based on the wavelet coe±cients. Ignoring wavelet coe±cients of higher order of resolution, the remaining wavelet coe±cients approximate a sample of independently and identically distributed normal variates with homogeneous variance within each level. The approximate MLE performs satisfactorily and provides a robust estimate for which the short memory component need not be speci ̄ed.