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:严格性是时间序列文献中用于得出二阶统计,如抽样自动变异和抽样自动变异等样本自动反射分布结果的常见假设。本文以薄弱的静态为重点,通过使用高萨近距离技术,得出了在脆弱条件下样本自动变异和抽样自变关系最大值的无症状分布,使用高萨近距离技术,证明了在薄弱条件下,样本自动变异和抽样自变关系最大值的无症状分布。通过安装一个(线性)自动递减模型到一个普遍薄弱的固定时间序列的参数估计的无症状理论得到了重新审视,并得出了自动递减系数估计最高值的高斯近似近似理论。要对所考虑的第二阶参数进行统计推论,则应用了一种靴式算法,即所谓的第二阶次单野靴陷阱程序的一致性得到了证明。与现有的靴带替代方法相比,第二阶次野靴带的有效性并不要求强加严格的固定条件或结构过程假设,如线性。良好的稳定样品是模拟的野系。</s>