Bootstrap prediction intervals for autoregressive time series
The calculation of interval forecasts for highly persistent autoregressive (AR) time series based on the bootstrap is considered. Three methods are considered for countering the small-sample bias of least-squares estimation for processes which have roots close to the unit circle: a bootstrap bias-corrected OLS estimator; the use of the RoyFuller estimator in place of OLS; and the use of the AndrewsChen estimator in place of OLS. All three methods of bias correction yield superior results to the bootstrap in the absence of bias correction. Of the three correction methods, the bootstrap prediction intervals based on the RoyFuller estimator are generally superior to the other two. The small-sample performance of bootstrap prediction intervals based on the RoyFuller estimator are investigated when the order of the AR model is unknown, and has to be determined using an information criterion.
bootstrapping bias correction autoregressive models