Bootstrap prediction intervals for autoregression using asymptotically mean-unbiased estimators

The use of asymptotically mean-unbiased parameter estimation is considered as a means of bias-correction, when bootstrap prediction interval is constructed for the autoregressive (AR) model with unknown lag order. Its computational efficiency facilitates application of the endogenous lag order bootstrapping algorithm. 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 small sample performances. These features are evident, especially when the sample size is small; when the model is near unit-root non-stationary; and for high order AR models where the range of order estimation is wide.