Large bandwidth asymptotics for Nadaraya–Watson auto-regression estimator

The Nadaraya–Watson auto-regression (NWAR) estimator is a popular method when nonparametric prediction is needed for the nonlinear auto-regression (NAR) model. For effective prediction, the choice of bandwidth for NWAR is critical as with other nonparametric regression methods. In this paper we study the mean integrated square error (MISE) for defining and searching for the optimal bandwidth hh of NWAR. In particular MISE is studied when hh is large. It will be shown that a large hh may be needed as dependency gets either too weak or too strong. Our result suggests that in practical situations optimal bandwidth search for NWAR is to be extended to the interval (0,∞)(0,∞) from the conventional (0, 1).