The Block-Block Bootstrap for Time Series

Abstract

This article proves that the block-block bootstrap of Andrews (2004) can be helpful to provide asymptotic refinements for the GMM estimator when autocorrelation structures of moment functions are unknown (i.e., incorporating the HAC covariance matrix) and when we allow for statistics that are inefficient. The asymptotic refinements of this block-block bootstrap in the time series context are shown to exist with the use of less restricted kernels than in the block bootstrap in Inoue and Shintani (2006), since they do not require to have a characteristic exponent larger than 2. The procedure allows to apply in practice kernels that guarantee that the HAC covariance matrix estimator is positive semidefinite, and to get asymptotic refinements at the same time.