Estimating a generalized long memory process

This paper considers the estimation of a two-parameter long memory process (the Gegenbauer process) that generalizes the popular one-parameter fractionally integrated process to allow for hyperbolic and sinusoidal decay in autocorrelations. Conditional sum of squares (CSS) estimation is suggested. We show that the estimator of one of the parameters converges, at a rate faster than the usual Op(T12), to the unit-root limiting distribution, i.e., a functional of Brownian motions. Simulation results on parameter estimation are provided to demonstrate the relevance of these theoretical results and ensuing computational problems.