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THE BOOTSTRAP OF THE MEAN FOR DEPENDENT HETEROGENEOUS ARRAYS

Published online by Cambridge University Press:  24 September 2002

Sílvia Gonçalves  and
Halbert White
Sílvia Gonçalves
Affiliation:
C.R.D.E, CIRANO, and Université de Montréal
Halbert White
Affiliation:
University of California, San Diego
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Abstract

Presently, conditions ensuring the validity of bootstrap methods for the sample mean of (possibly heterogeneous) near epoch dependent (NED) functions of mixing processes are unknown. Here we establish the validity of the bootstrap in this context, extending the applicability of bootstrap methods to a class of processes broadly relevant for applications in economics and finance. Our results apply to two block bootstrap methods: the moving blocks bootstrap of Künsch (1989, Annals of Statistics 17, 1217–1241) and Liu and Singh (1992, in R. LePage & L. Billiard (eds.), Exploring the Limits of the Bootstrap, 224–248) and the stationary bootstrap of Politis and Romano (1994a, Journal of the American Statistical Association 89, 1303–1313). In particular, the consistency of the bootstrap variance estimator for the sample mean is shown to be robust against heteroskedasticity and dependence of unknown form. The first-order asymptotic validity of the bootstrap approximation to the actual distribution of the sample mean is also established in this heterogeneous NED context.

Type
Research Article
Information
Econometric Theory , Volume 18 , Issue 6 , December 2002 , pp. 1367 - 1384
Copyright
© 2002 Cambridge University Press

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