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The non-linear autoregressive (NLAR) model plays an important role inmodeling and predicting time series. One-step ahead prediction isstraightforward using the NLAR model, but the multi-step ahead prediction iscumbersome. For instance, iterating the one-step ahead predictor is aconvenient strategy for linear autoregressive (LAR) models, but it issuboptimal under NLAR. In this paper, we first propose a simulation and/orbootstrap algorithm to construct optimal point predictors under an $L_1$ or$L_2$ loss criterion. In addition, we construct bootstrap prediction intervalsin the multi-step ahead prediction problem; in particular, we develop anasymptotically valid quantile prediction interval as well as a pertinentprediction interval for future values. In order to correct the undercoverage ofprediction intervals with finite samples, we further employ predictive -- asopposed to fitted -- residuals in the bootstrap process. Simulation studies arealso given to substantiate the finite sample performance of our methods.

Bootstrap Prediction Inference of Non-linear Autoregressive Models