Bootstrap Prediction Inference of Non-linear Autoregressive Models
Abstract
The non-linear 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 paper, 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. In order to correct the undercoverage of prediction intervals with finite samples, we further employ predictive -- as opposed to fitted -- residuals in the bootstrap process. Simulation studies are also given to substantiate the finite sample performance of our methods.
Cite
@article{arxiv.2306.04126,
title = {Bootstrap Prediction Inference of Non-linear Autoregressive Models},
author = {Kejin Wu and Dimitris N. Politis},
journal= {arXiv preprint arXiv:2306.04126},
year = {2023}
}