Bootstrap Prediction Inference of Non-linear Autoregressive Models

Kejin Wu; Dimitris N. Politis

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arXiv · 2306.04126

Bootstrap Prediction Inference of Non-linear Autoregressive Models

Kejin Wu·Dimitris N. Politis

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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 $L_1$ or $L_2$ 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.

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Kejin Wu, Dimitris N. Politis. 2023-06-07. Bootstrap Prediction Inference of Non-linear Autoregressive Models. https://arxiv.org/abs/2306.04126

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