Bootstrap prediction intervals for linear, nonlinear, and nonparametric autoregressions

In order to construct prediction intervals without the combersome--and typically unjustifiable--assumption of Gaussianity, some form of resampling is necessary. The regression set-up has been well-studies in the literature but time series prediction faces additional difficulties. The paper at hand focuses on time series that can be modeled as linear, nonlinear or nonparametric autoregressions, and develops a coherent methodology for the constructuion of bootstrap prediction intervals. Forward and backward bootstrap methods for using predictive and fitted residuals are introduced and compared. We present detailed algorithms for these different models and show that the bootstrap intervals manage to capture both sources of variability, namely the innovation error as well as essimation error. In simulations, we compare the prediction intervals associated with different methods in terms of their acheived coverage level and length of interval.Â