Bootstrap prediction inference of nonlinear autoregressive models
针对非线性自回归模型的多步预测难题，提出基于模拟和Bootstrap的最优点预测与区间预测方法，并用预测残差修正小样本覆盖不足，适用于经济时间序列预测。
The nonlinear autoregressive (NLAR) model plays an important role in modeling and predicting time series. One‐step ahead prediction is straightforward using the NLAR model, but the multi‐step ahead prediction is cumbersome. For instance, iterating the one‐step ahead predictor is a convenient strategy for linear autoregressive (LAR) models, but it is suboptimal under NLAR. In this article, we first propose a simulation and/or bootstrap algorithm to construct optimal point predictors under an or loss criterion. In addition, we construct bootstrap prediction intervals in the multi‐step ahead prediction problem; in particular, we develop an asymptotically valid quantile prediction interval as well as a pertinent prediction interval for future values. To correct the undercoverage of prediction intervals with finite samples, we further employ predictive – as opposed to fitted – residuals in the bootstrap process. Simulation and empirical studies are also given to substantiate the finite sample performance of our methods.