Parameter estimation in low order fractionally differenced ARMA processes

Abstract

A class of regression type estimators of the parameterd in a fractionally differencedARMA (p, q) process is introduced. This class is an extension of the estimator considered by Geweke and Porter-Hudak. In a simulation study, we compared three estimators from this class together with two approximate maximum likelihood estimators which are based on two separate approximations to the likelihood. One approximation ignores the determinant term in the likelihood and the other includes a compensating factor for the determinant. When the determinant term is included, the estimate tends to be much less biased and is in general superior to the other estimate. The approximate maximum likelihood estimator out performed, by a large margin, the regression type estimators for pureARIMA (0,d,0) processes. However, forARIMA (1,d,1) processes, a regression type estimator turned out to be the best for realizations of length 400 in 3 out of the 5 cases we tried.