Efficient Regression in Time Series Partial Linear Models

This paper studies efficient estimation of partial linear regression in time series models. In particular, it combines two topics that have attracted a good deal of attention in econometrics, viz. spectral regression and partial linear regression, and proposes an efficient frequency domain estimator for partial linear models with serially correlated residuals. A nonparametric treatment of regression errors is permitted so that it is not necessary to be explicit about the dynamic specification of the errors other than to assume stationarity. A new concept of weak dependence is introduced based on regularity conditions on the joint density. Under these and some other regularity conditions, it is shown that the spectral estimator is root-n-consistent, asymptotically normal, and asymptotically efficient.