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BLOCK BOOTSTRAP CONSISTENCY UNDER WEAK ASSUMPTIONS
Published online by Cambridge University Press: 01 February 2018
Abstract
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This paper weakens the size and moment conditions needed for typical block bootstrap methods (i.e., the moving blocks, circular blocks, and stationary bootstraps) to be valid for the sample mean of Near-Epoch-Dependent (NED) functions of mixing processes; they are consistent under the weakest conditions that ensure the original NED process obeys a central limit theorem (CLT), established by De Jong (1997, Econometric Theory 13(3), 353–367). In doing so, this paper extends De Jong’s method of proof, a blocking argument, to hold with random and unequal block lengths. This paper also proves that bootstrapped partial sums satisfy a functional CLT (FCLT) under the same conditions.
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Footnotes
I would like to thank Helle Bunzel, Dimitris Politis, Robert Taylor, and three anonymous referees for their comments and feedback on earlier versions of this paper.
References
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