It is common to assess the "memory strength" of a stationary process looking at how fast the normalized log-determinant of its covariance submatrices (i.e., entropy rate) decreases. In this work, we propose an alternative characterization in terms of the normalized trace-inverse of the covariance submatrices. We show that this sequence is monotonically non-decreasing and is constant if and only if the process is white. Furthermore, while the entropy rate is associated with one-sided prediction errors (present from past), the new measure is associated with two-sided prediction errors (present from past and future). This measure can be used as an alternative to Burg's maximum-entropy principle for spectral estimation. We also propose a counterpart for non-stationary processes, by looking at the average trace-inverse of subsets.

中文翻译：

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协方差子矩阵的迹线逆的单调性和双向预测

通常会评估固定过程的“内存强度”，以查看其协方差子矩阵的标准化对数决定因素（即熵率）下降的速度。在这项工作中，我们提出了关于协方差子矩阵的归一化迹线逆的另一种表征。我们证明该序列是单调非递减的，并且当且仅当过程为白色时才是恒定的。此外，尽管熵率与单边预测误差（过去的结果）相关联，但新度量与单边预测误差（过去和将来的结果）相关联。此度量可以用作Burg最大熵原理进行频谱估计的替代方法。通过查看子集的平均跟踪逆，我们还为非平稳过程提出了一个对应项。