Kernel smoothed prediction intervals for ARMA models

The procedures of estimating prediction intervals for ARMA processes can be divided into model based methods and empirical methods. Model based methods require knowledge of the model and the underlying innovation distribution. Empirical methods are based on sample forecast errors. In this paper we apply nonparametric quantile regression to empirical forecast errors using lead time as regressor. Using this method there is no need for a distributional assumption. But for the special data pattern in this application a double kernel method which allows smoothing in two directions is required. An estimation algorithm is presented and applied to some simulation examples.