The wild tapered block bootstrap

In this paper, a new resampling procedure, called the wild tapered block bootstrap, is introduced as a means of calculating standard errors of estimators and constructing confidence regions for parameters based on dependent heterogeneous data. The method consists in tapering each overlapping block of the series first, then applying the standard wild bootstrap for independent and heteroscedastic distributed observations to overlapping tapered blocks in an appropriate way. It preserves the favorable bias and mean squared error properties of the tapered block bootstrap, which is the state-of-the-art block-based method in terms of asymptotic accuracy of variance estimation and distribution approximation. For stationary time series, the asymptotic validity, and the favorable bias properties of the new bootstrap method are shown in two important cases: smooth functions of means, and M-estimators. The first-order asymptotic validity of the tapered block bootstrap as well as the wild tapered block bootstrap approximation to the actual distribution of the sample mean is also established when data are assumed to satisfy a near epoch dependent condition. The consistency of the bootstrap variance estimator for the sample mean is shown to be robust against heteroskedasticity and dependence of unknown form. Simulation studies illustrate the finite-sample performance of the wild tapered block bootstrap. This easy to implement alternative bootstrap method works very well even for moderate sample sizes.