Bootstrap Prediction Bands for Functional Time Series

A bootstrap procedure for constructing prediction bands a stationary functional time series is proposed. The exploits general vector autoregressive representation of the time-reversed Fourier coefficients appearing in Karhunen–Loève process. It generates backward-in-time replicates that adequately mimic dependence structure underlying process model-free way and have same conditionally fixed curves at end each pseudo-time series. error distribution then calculated as difference between model-free, bootstrap-generated future observations forecasts obtained from model used prediction. This allows estimated to account innovation estimation errors associated with possible due misspecification. We establish asymptotic validity estimating conditional interest, we also show enables construction achieve (asymptotically) desired coverage. Prediction based on consistent studentized are introduced. Such allow taking more appropriately into local uncertainty Through simulation study analysis two datasets, demonstrate capabilities good finite-sample performance proposed method.