Bootstrap Prediction Intervals for Autoregressive Models Based on Asymptotically Mean-Unbiased Parameter Estimators

The use of asymptotically mean-unbiased estimation is considered as a means of biascorrection, when bootstrap prediction interval is constructed for autoregressive (AR) models with unknown lag order. Its computational efficiency enables application of the endogenous lag order bootstrap algorithm to prediction intervals. Extensive Monte Carlo experiments are conducted using a number of stationary and near unit-root AR models. It is found that bias-correction based on asymptotically mean-unbiased estimation substantially improves small sample properties of bootstrap prediction intervals. In particular, the endogenous lag order bootstrap interval shows highly desirable performances. These features are evident, especially when the sample size is small, the model is near unit-root non-stationary, and the range of order estimation is wide.