The goal of this paper is to obtain expectation bounds for the deviation of large sample autocovariance matrices from their means under weak data dependence. While the accuracy of covariance matrix estimation corresponding to independent data has been well understood, much less is known in the case of dependent data. We make a step toward filling this gap and establish deviation bounds that depend only on the parameters controlling the “intrinsic dimension” of the data up to some logarithmic terms. Our results have immediate impacts on high-dimensional time-series analysis, and we apply them to high-dimensional linear VAR(d) model, vector-valued ARCH model, and a model used in Banna et al. (Random Matrices Theory Appl 5(2):1650006, 2016).

中文翻译：

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依赖下大型自协方差矩阵的矩界

本文的目标是获得大样本自协方差矩阵在弱数据依赖性下与其均值的偏差的期望界限。虽然与独立数据对应的协方差矩阵估计的准确性已被很好地理解，但在相关数据的情况下却知之甚少。我们朝着填补这一空白迈进了一步，并建立了偏差界限，该界限仅取决于控制数据“内在维度”的参数，直到某些对数项。我们的结果对高维时间序列分析有直接影响，我们将它们应用于高维线性 VAR(d) 模型、向量值 ARCH 模型和 Banna 等人使用的模型。（随机矩阵理论应用 5(2):1650006, 2016）。