论文标题
关于高维时间序列的频域检测
On the frequency domain detection of high dimensional time series
论文作者
论文摘要
在本文中，我们解决了频域中检测问题的问题，该问题是由M X K MIMO滤波器的输出建模的，该输出由K维高斯白噪声驱动，并受到添加剂M维高斯色彩的噪声的干扰。我们考虑基于光谱相干矩阵（SCM）的测试统计研究，作为在N样品上观察到的时间序列的平滑周期图基质的重新归一化，并以N样品的跨度B进行。为此，我们考虑了渐近状态，我们考虑m，b，b，n在某些特定的特定速率上均保持固定的固定速率，而n commente n commented nep固定。我们证明，SCM可以通过相关的Wishart矩阵在运算符规范中近似，为此，随机矩阵理论（RMT）提供了对特征值的渐近行为的精确描述。然后利用这些结果来研究基于SCM最大特征值的测试的一致性，并提供一些数值插图来评估此类测试的统计性能。
In this paper, we address the problem of detection, in the frequency domain, of a M-dimensional time series modeled as the output of a M x K MIMO filter driven by a K-dimensional Gaussian white noise, and disturbed by an additive M-dimensional Gaussian colored noise. We consider the study of test statistics based of the Spectral Coherence Matrix (SCM) obtained as renormalization of the smoothed periodogram matrix of the observed time series over N samples, and with smoothing span B. To that purpose, we consider the asymptotic regime in which M, B, N all converge to infinity at certain specific rates, while K remains fixed. We prove that the SCM may be approximated in operator norm by a correlated Wishart matrix, for which Random Matrix Theory (RMT) provides a precise description of the asymptotic behaviour of the eigenvalues. These results are then exploited to study the consistency of a test based on the largest eigenvalue of the SCM, and provide some numerical illustrations to evaluate the statistical performance of such a test.
