Median unbiased forecasts for highly persistent autoregressive processes

This paper considers the construction of median unbiased forecasts for near-integrated autoregressive processes. It derives the appropriately scaled limiting distribution of the deviation of the forecast from the true conditional mean. The dependence of the limiting distribution on nuisance parameters precludes the use of the standard asymptotic and bootstrap methods for bias correction. We propose a bootstrap method that generates samples backward in time and approximates the median function of the predictive distribution on a grid of values for the nuisance parameter. The method can be easily adapted to approximate any quantile of the conditional predictive distribution.