Bootstrap prediction intervals for time series models with hetroscedastic errors

In this paper,we propose two bootstrap procedures to construct prediction intervals for autoregressive fractionally integrated moving average with conditionally hetroscedastic errors (arfima-garch) models. the first method is based on the model based bootstrap,in which the order of the model is assumed to be known. the second bootstrap method is based on the idea of approximating the arfima part by an ar model. in modeling the arfima-garch model,the first step is to determine the order of arfima part and determination the order of arfima model is a complicated task. to simplify the model building procedure,we approximate the arfima part of the arfima-garch model by an ar(p) model and fit an ar-garch model instead of arfima-garch model. the methodology has also been applied to arma-garch models. to check the performance of the proposed methods,we perform simulation study. © 2017 pakistan journal of statistics.