  In this paper for the first time the nonparametric autoregression estimation
problem for the quadratic risks is considered. To this end we develop a new
adaptive sequential model selection method based on the efficient sequential
kernel estimators proposed by Arkoun and Pergamenshchikov (2016). Moreover, we
develop a new analytical tool for general regression models to obtain the non
asymptotic sharp or- acle inequalities for both usual quadratic and robust
quadratic risks. Then, we show that the constructed sequential model selection
proce- dure is optimal in the sense of oracle inequalities.
