Diagnostics for the Bootstrap and Fast Double Bootstrap

The bootstrap is typically much less reliable in the context of time-series models with serial correlation of unknown form than it is when regularity conditions for the conventional IID bootstrap, based on resampling, apply. It is therefore useful for practitioners to have available diagnostic techniques capable of evaluating bootstrap performance in specific cases. The techniques suggested in this paper are closely related to the fast double bootstrap, and, although they inevitably rely on simulation, they are not computationally intensive. They can also be used to gauge the performance of the fast double bootstrap itself. Examples of bootstrapping time series are presented which illustrate the diagnostic procedures, and show how the results can cast light on bootstrap performance.