On the estimation of long-memory time series models

A novel Pseudo-Linear method for the estimation of Fractionally Integrated ARMA (ARFIMA) models, that are capable of representing combined long and short term dependencies. is introduced. The method is based upon the relationship of the AR/MA parameters and the coefficients of the fractional power operator binomial series expansion with the model´s inverse function. These lead to the formulation of a special-form regression problem that can be decomposed into a univariate non-linear and a multivariate linear regression, and may be thus tackled via a pseudo-linear procedure. This decomposition leads to computational simplicity, elimination of the need for initial guess parameter values, and drastic simplifications in the detection and handling of potential local extrema problems. The method´s strong consistency is established. and its performance characteristics are demonstrated via Monte Carlo experiments and comparisons with a Maximum Likelihood scheme.