  Conditional expectations given past observations in stationary time series
are usually estimated directly by kernel estimators, or by plugging in kernel
estimators for transition densities. We show that, for linear and nonlinear
autoregressive models driven by independent innovations, appropriate smoothed
and weighted von Mises statistics of residuals estimate conditional
expectations at better parametric rates and are asymptotically efficient. The
proof is based on a uniform stochastic expansion for smoothed and weighted von
Mises processes of residuals. We consider, in particular, estimation of
conditional distribution functions and of conditional quantile functions.
