Efficient inference for autoregressive coefficients in the presence of trends

Time series often contain unknown trend functions and unobservable error terms. As is known, Yule–Walker estimators are asymptotically efficient for autoregressive time series. The focus of this article is the Yule–Walker estimators for time series with trends. A nonparametric detrending procedure is proposed. It is concluded that the asymptotic properties of the Yule–Walker estimators of autoregressive coefficients are not altered by the detrending procedure. The results of the simulation studies and real data application corroborate the asymptotic theory.