In this paper we obtain root-n consistency and functional central limittheorems in weighted L 1-spaces for plug-in estimators of thetwo-step transition density in the classical stationary linear autoregressivemodel of order one, assuming essentially only that the innovation density has bounded variation. We also show that plugging in a properly weighted residual-basedkernel estimator for the unknown innovation densityimproves on plugging in an unweighted residual-based kernel estimator. These weights are chosen to exploit thefact that the innovations have mean zero.If an efficient estimator for the autoregression parameter is used,then the weighted plug-in estimator for the two-step transition density is efficient. Our approach generalizes to invertible linear processes.
