Diagnostics for the bootstrap and fast double bootstrap

ABSTRACT

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

KEYWORDS:

• Autocorrelation of unknown form
• bootstrap
• diagnostics for bootstrap
• fast double bootstrap
• time series

2010 MATHEMATICS SUBJECT CLASSIFICATION:

• C10
• C15
• C22
• C63

Acknowledgments

This research was supported by the Canada Research Chair program (Chair in Economics, McGill University) and by a grant from the Fonds de Recherche du Québec - Société et Culture. I am grateful to two anonymous referees, seminar participants at Emory University, the Universities of Aarhus, York, and Durham for helpful comments, and especially to James MacKinnon.

Notes

¹The actual running time was only between two and two and a half minutes, because 50 cores were used in parallel.

²The constant estimates the expectation of τ* minus that of τ multiplied by the correlation between the two.