  To address the difficult problem of multi-step ahead prediction of
non-parametric autoregressions, we consider a forward bootstrap approach.
Employing a local constant estimator, we can analyze a general type of
non-parametric time series model, and show that the proposed point predictions
are consistent with the true optimal predictor. We construct a quantile
prediction interval that is asymptotically valid. Moreover, using a debiasing
technique, we can asymptotically approximate the distribution of multi-step
ahead non-parametric estimation by bootstrap. As a result, we can build
bootstrap prediction intervals that are pertinent, i.e., can capture the model
estimation variability, thus improving upon the standard quantile prediction
intervals. Simulation studies are given to illustrate the performance of our
point predictions and pertinent prediction intervals for finite samples.
