Bias-correction and endogenous lag order algorithm for bootstrap prediction intervals

Pan and Politis present an informative and comprehensive review of the bootstrap methods for constructing prediction intervals for autoregressive (AR) time series. In this discussion, I call attention to the bias-correction and endogenous lag order algorithms, which can be added to the bootstrap procedures. They can be implemented with resampling based on the forward AR model, backward AR model, and predictive residuals. Using a long time series of price–earnings ratio, I demonstrate that these additional techniques substantially improve the small sample performance of the bootstrap prediction intervals for linear AR models.