In this article, maximum deviations of sample autocovariances and autocorrelations from their theoretical counterparts over an increasing set of lags are considered. The asymptotic distribution of such statistics for physically dependent stationary time series, which is of Gumbel type, only depends on second-order properties of the underlying time series. Since the autoregressive sieve bootstrap is able to mimic the second-order structure asymptotically correctly it is an obvious problem whether the autoregressive (AR) sieve bootstrap, which has been shown to work for a number of relevant statistics in time series analysis, asymptotically works for maximum deviations of autocovariances and autocorrelations as well. This article shows that the question can be answered positively. Moreover, potential applications including spectral density estimation and an investigation of finite sample properties of the AR-sieve bootstrap proposal by simulation are given.

中文翻译：

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基于自回归筛选自举法的自协方差同时推断

在本文中，考虑了随着滞后的增加，样本自协方差和自相关与其理论对应物的最大偏差。Gumbel 类型的物理相关平稳时间序列的此类统计量的渐近分布仅取决于基础时间序列的二阶属性。由于自回归筛自举能够渐近正确地模拟二阶结构，因此自回归 (AR) 筛自举已被证明适用于时间序列分析中的许多相关统计数据，是否渐近适用于自协方差和自相关的最大偏差也是如此。这篇文章表明，这个问题可以得到肯定的回答。而且，