  We propose kernel estimator for the distribution function of unobserved
errors in autoregressive time series, based on residuals computed by estimating
the autoregressive coefficients with the Yule-Walker method. Under mild
assumptions, we establish oracle efficiency of the proposed estimator, that is,
it is asymptotically as efficient as the kernel estimator of the distribution
function based on the unobserved error sequence itself. Applying the result of
Wang, Cheng and Yang [J. Nonparametr. Stat. 25 (2013) 395-407], the proposed
estimator is also asymptotically indistinguishable from the empirical
distribution function based on the unobserved errors. A smooth simultaneous
confidence band (SCB) is then constructed based on the proposed smooth
distribution estimator and Kolmogorov distribution. Simulation examples support
the asymptotic theory.
