The dependent wild bootstrap

We propose a new resampling procedure, the dependent wild bootstrap, for stationary time series. As a natural extension of the traditional wild bootstrap to time series setting, the dependent wild bootstrap offers a viable alternative to the existing block-based bootstrap methods, whose properties have been extensively studied over the last two decades. Unlike all of the block-based bootstrap methods, the dependent wild bootstrap can be easily extended to irregularly spaced time series with no implementational difficulty. Furthermore, it preserves the favorable bias and mean squared error property 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. The consistency of the dependent wild bootstrap in distribution approximation is established under the framework of the smooth function model. In addition, we obtain the bias and variance expansions of the dependent wild bootstrap variance estimator for irregularly spaced time series on a lattice. For irregularly spaced nonlattice time series, we prove the consistency of the dependent wild bootstrap for variance estimation and distribution approximation in the mean case. Simulation studies and an empirical data analysis illustrate the finite-sample performance of the dependent wild bootstrap. Some technical details and tables are included in the online supplemental material.