Semiparametric estimation in time-series regression with long-range dependence

We consider semiparametric estimation in time-series regression in the presence of long-range dependence in both the errors and the stochastic regressors. A central limit theorem is established for a class of semiparametric frequency domain-weighted least squares estimates, which includes both narrow-band ordinary least squares and narrow-band generalized least squares as special cases. The estimates are semiparametric in the sense that focus is on the neighbourhood of the origin, and only periodogram ordinates in a degenerating band around the origin are used. This setting differs from earlier studies on time-series regression with long-range dependence, where a fully parametric approach has been employed. The generalized least squares estimate is infeasible when the degree of long-range dependence is unknown and must be estimated in an initial step. In that case, we show that a feasible estimate which has the same asymptotic properties as the infeasible estimate, exists. By Monte Carlo simulation, we evaluate the finite-sample performance of the generalized least squares estimate and the feasible estimate.