Advances in the Estimation of Fractionally Integrated Models

Data in the economic and financial spheres often exhibit dynamic patterns characterized by a long lasting response to past shocks. The correct modelling of such long range dependence is of paramount importance, both in the production of accurate forecasts over long term horizons and in the isolation of long run equilibrium relationships. While the convention in the area has been to adopt complete parametric specifications for the dynamics in the time series, semi-parametric approaches have also featured. This thesis contributes to both of these lines of research, exploring the consequences for parametric estimation of mis-specification of the short memory dynamics and developing a bias-corrected semi-parametric estimator of the long memory parameter.