Abstract The stationary bootstrap method is popularly used to compute the standard errors or confidence regions of estimators, generated from time processes exhibiting weakly dependent stationarity. Most previous stationary bootstrap methods have focused on studying large-sample properties of stationary bootstrap inference about a sample mean under short-range dependence. For long-range dependence, recent studies have investigated the properties of block bootstrap methods using overlapping and non-overlapping blocking techniques with fixed block lengths. However, the characteristics of a stationary bootstrap with random block lengths are less well-known under long-range dependence. We investigate the asymptotic property of a stationary bootstrap variance estimator for a sample mean under long-range dependence. Our theoretical and simulation results indicate that the stationary bootstrap method does not have n − consistency for stationary and long-range dependent time processes.

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关于长程依赖下的平稳自举方差估计器的注记

摘要 平稳自举方法广泛用于计算估计量的标准误差或置信区间，这些估计量是由表现出弱相关平稳性的时间过程生成的。大多数先前的平稳自举方法都专注于研究关于短程依赖下样本均值的平稳自举推理的大样本特性。对于长距离依赖，最近的研究调查了块自举方法的特性，该方法使用具有固定块长度的重叠和非重叠块技术。然而，在长期依赖下，具有随机块长度的固定自举的特征鲜为人知。我们研究了长期依赖下样本均值的平稳自举方差估计量的渐近性质。