Bootstrap prediction inference of nonlinear autoregressive models

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 strateg...

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Bibliographic Details
Published in:Journal of time series analysis 2024-09, Vol.45 (5), p.800-822
Main Authors: Wu, Kejin, Politis, Dimitris N.
Format: Article
Language:English
Subjects:
Algorithms
Asymptotic methods
Autoregressive models
Bootstrap
Intervals
NLAR forecasting
Performance prediction
pertinence prediction
Simulation
Time series
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Summary: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 L1 or L2 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.
ISSN:0143-9782
1467-9892
DOI:10.1111/jtsa.12739