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.

翻译：针对非参数自回归模型多步超前预测这一难题，我们提出了一种前向Bootstrap方法。通过采用局部常数估计量，我们能够分析一类广义的非参数时间序列模型，并证明所提出的点预测与真实最优预测具有一致性。我们构建了渐近有效的分位数预测区间。此外，利用去偏技术，我们可通过Bootstrap渐近逼近多步超前非参数估计的分布。由此构建的Bootstrap预测区间具有相关性，即能够捕获模型估计的变异性，从而优于标准的分位数预测区间。通过仿真研究，我们展示了所提出的点预测及相关预测区间在有限样本下的性能。