Two-Point Dependent Wild Bootstrap for Weakly Dependent Estimating Equations

2026-09-26

AI Summary

This study addresses the insufficient inference accuracy of estimating equations under weak dependence by proposing a two-point correlated wild bootstrap method. Built upon a Gaussian copula framework, the approach independently specifies two-point marginal distributions and latent serial dependence structures via Rademacher or Mammen multipliers, while nesting a classical IID bootstrap to achieve heteroskedasticity and autocorrelation consistent (HAC) covariance matching. The first-order validity of the proposed method is theoretically established. Monte Carlo simulations further demonstrate that the Rademacher scheme yields superior size control in finite samples. Overall, this work provides a high-precision inference tool for hypothesis testing in weakly dependent models, including generalized method of moments (GMM) estimation.

Abstract

This paper develops a general two-point dependent wild bootstrap (DWB) for weakly dependent estimating equations. Its key feature is that the two-point marginal distribution and the latent serial dependence specification can be chosen separately. The construction combines a normalized two-point distribution with a stationary latent Gaussian process via a Gaussian copula transformation, includes dependent Rademacher and Mammen multipliers, and nests the classical iid two-point wild bootstrap as the serially independent case. The induced multiplier autocovariances determine the lag weights in a corresponding heteroskedasticity- and autocorrelation-consistent (HAC) covariance estimator, which coincides exactly with the conditional covariance of the bootstrap estimating-equation sum. We establish first-order bootstrap validity for asymptotically linear estimators by showing that the matched-HAC estimator consistently estimates the long-run covariance and that the bootstrap estimating-equation sum converges conditionally to the same Gaussian limit as its original-sample counterpart, yielding valid HAC-studentized $z$-tests and the corresponding Wald and Lagrange multiplier tests. Monte Carlo experiments in nonlinear generalized method of moments (GMM) and linear regression show that Rademacher DWB generally provides more accurate finite-sample size control for $z$-tests than the Mammen and Gaussian DWB. A GMM application to a nonlinear short-rate mean-reversion model illustrates the practical relevance of the proposed two-point DWB.

Problem

• wild bootstrap
• weak dependence
• estimating equations
• HAC covariance
• statistical inference

Innovation

• Dependent Wild Bootstrap
• Estimating Equations
• Gaussian Copula
• HAC Covariance Estimator
• Generalized Method of Moments