UC San Diego

We construct bootstrap prediction intervals for linear autoregressions, nonlinear autoregressions, nonparametric autoregressions and Markov processes. Several forward and backward bootstrap methods using predictive residuals and fitted residuals are introduced and applied to those time series. We describe exact algorithms for these different models and show that the bootstrap intervals properly estimate the distribution of the future values. In simulations using standard time series models, we compare the prediction intervals of different methods with regards to coverage level and length of interval