Preliminary test estimation for regression models with long-memory disturbance

For a class of time series regression models with long-memory disturbance, we are interested in estimation of a subset of the regression coefficient vector and spectral parameter of the residual process when the complementary subset is suspected to be close to 0. In this situation, we evaluate the mean square errors of the restricted and unrestricted MLE and a preliminary test estimator when the complementary parameters are contiguous to zero vector. The results are expressed in terms of the regression spectra and the residual spectra. Since we assume long-memory dependence for the disturbance, the asymptotics are much different from the case of i.i.d. disturbance. Numerical studies elucidate some interesting features of regression and long-memory structures.