THE BOOTSTRAP OF THE MEAN FOR DEPENDENT HETEROGENEOUS ARRAYS

S lvia Gon alves and Halbert White

Econometric Theory, 2002, vol. 18, issue 06, pages 1367-1384

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 K nsch (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.

Date: 2002
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Working Paper: The Bootstrap of the Mean for Dependent Heterogeneous Arrays (2001)
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