Investigating some estimators of the fractional degree of differencing, in long memory time series

Abstract

We investigated three estimators of the fractional parameter d, in long memory time series. Discussed in [4], the rst estimator is based on a regression analysis using the periodogram of the long memory series; the second estimator which is discussed in [11, 10], is based on a regression analysis using a lag-window spectral density estimator; the third estimator performs a maximum likelihood estimation (MLE) of d using the fast and accurate method of [8]. To conduct our investigation, we generated synthetic ARFIMA(p; d; q) samples where d = :25 and d = :45. Computational results showed that in general the MLE method performs better in large samples whereas the [4] proposed estimator performs better in small samples. Yet, the estimator in [11, 10] behaves better than that proposed by [4] in large samples. While the MLE has the smallest standard errors in both small and large samples, the standard errors of the [4] approach are the largest.