The asymptotic behaviour of Linear Spectral Statistics (LSS) of the smoothed periodogram estimator of the spectral coherency matrix of a complex Gaussian high-dimensional time series (yn) n$\in$Z with independent components is studied under the asymptotic regime where both the dimension M of y and the smoothing span of the estimator grow to infinity at the same rate. It is established that the estimated spectral coherency matrix is close from the sample covariance matrix of an independent identically N C (0, I M) distributed sequence, and that its empirical eigenvalue distribution converges towards the Marcenko-Pastur distribution. This allows to conclude that each LSS has a deterministic behaviour that can be evaluated explicitely. Using concentration inequalities, it is shown that the order of magnitude of the deviation of each LSS from its deterministic approximation is of the order of M N where N is the sample size. Numerical simulations suggest that these results can be used to test whether a large number of time series are uncorrelated or not. MSC 2010 subject classifications: Primary 60B20, 62H15; secondary 62M15.

翻译：光谱谱统计(LSS) 平滑时期光谱统计(LSS) 的无线行为, 平滑的光谱显示光度统计(LSS), 光谱共振分布序列的光谱相容矩阵测深器, 具有独立元件的复合高森高维时间序列( yn) n$/ in$Z 的光谱共振矩阵的光谱共振矩阵, 在无线系统制度下进行研究, 该体系的维度M y 的维度和光滑度范围以相同的速度增长到无限。 已经确定, 估计的光谱共振矩阵与一个独立、 完全相同的 N C (0, I M) 分布序列的样本共变基质矩阵十分接近, 其实验性电子元值分布会与 Marcenko- Pastur 分布相交汇。 这可以得出结论, 每个光谱系统都有可明确评估的确定性行为。 使用浓度不平等性, 显示每个光谱显示每个光谱系统偏离其确定性近度大小的大小是M N N 的顺序。 N 的 m 。 和样本大小 。 。 。 。 数值模拟模拟模拟显示这些结果可以用来测试大量时间序列是否不相交替的6020 ; MAS 2010 62 MC 主题 。