Time Series Regression with Long Range Dependence - (Now published in 'Annals of Statistics', 25, (1997)pp.2054-2083.)

A general limit theorem is established for time series regression estimates which include generalized least squares, in the presence of long range dependence in both errors and stochastic regressors. The setting and results differ significantly from earlier work on regression with long range dependent errors. Spectral singularities are permitted at any frequency. When sufficiently strong spectral singularities in the error and a regressor coincide at the same frequency, least squares need no longer be n?-consistent, where n is sample size. However, we show that our class of estimates is n?-consistent and asymptotically normal. In the generalized least squares case we show that efficient estimation is still possible when the error autocorrelation is known only up to finitely many parameters. We include a Monte Carlo study of finite sample performance and provide an extension to nonlinear least squares.