Strict stationarity is a common assumption used in the time series literature in order to derive asymptotic distributional results for second-order statistics, like sample autocovariances and sample autocorrelations. Focusing on weak stationarity, this paper derives the asymptotic distribution of the maximum of sample autocovariances and sample autocorrelations under weak conditions by using Gaussian approximation techniques. The asymptotic theory for parameter estimation obtained by fitting a (linear) autoregressive model to a general weakly stationary time series is revisited and a Gaussian approximation theorem for the maximum of the estimators of the autoregressive coefficients is derived. To perform statistical inference for the second order parameters considered, a bootstrap algorithm, the so-called second-order wild bootstrap, is applied. Consistency of this bootstrap procedure is proven. In contrast to existing bootstrap alternatives, validity of the second-order wild bootstrap does not require the imposition of strict stationary conditions or structural process assumptions, like linearity. The good finite sample performance of the second-order wild bootstrap is demonstrated by means of simulations.

翻译：严格平稳性是时间序列文献中为推导二阶统计量（如样本自协方差和样本自相关系数）渐近分布结果而常用的假设。本文聚焦弱平稳性，利用高斯逼近技术，在弱条件下推导了样本自协方差和样本自相关系数最大值的渐近分布。通过将（线性）自回归模型拟合至一般弱平稳时间序列所获参数估计的渐近理论得到重新审视，并推导了自回归系数估计量最大值的渐近高斯逼近定理。为对上述二阶参数进行统计推断，本文采用了一种称为二阶野自助法的自举算法，并证明了该自举程序的一致性。与现有自举替代方法不同，二阶野自助法的有效性无需施加严格平稳条件或线性等结构性过程假设。通过仿真实验验证了二阶野自助法在有限样本下的良好表现。