We study training-free fixed-length descriptors for multivariate time series and ask not merely whether such a descriptor performs well, but when it can be expected to work at all. Our object of study is $D(τ)$, built from a time-lagged correlation matrix truncated at the Marchenko-Pastur edge so that only signal-bearing eigenvalues survive and classified by cosine similarity to class centroids with zero learned parameters. The central contribution is not the descriptor but a falsifiable applicability criterion for it. Working from a stationary Gaussian VAR(1) model, we argue that $D(τ)$ separates two classes when the signals are approximately stationary and the class information lives in their cross-channel temporal coupling rather than in marginal per-channel power. We derive, semi-formally, three consequences: a distinguishability condition, why the static ($τ=0$) covariance collapses to chance, and why a stationary but power-discriminated paradigm defeats the descriptor. The criterion is operational: a two-part pre-flight test -- an augmented Dickey-Fuller stationarity check and a power-baseline saturation check -- predicts applicability before any training. We validate both halves on a mixed assortment. On four paradigms that satisfy the criterion (Sleep-EDF, BCI-IV-2a, MIT-BIH, ESC-50) the descriptor is competitive with strong baselines at a fraction of their cost, reaching $88.5\pm4.5\%$ under 20-subject leave-one-subject-out on Sleep-EDF on a single CPU thread. On three that violate it -- non-stationary ERPs, and financial-volatility and wearable-stress regimes that are power-discriminated -- it fails exactly as the pre-flight predicts, and these negatives are the more informative half. We are explicit that $D(τ)$ is not the most accurate representation; its value is a compact, training-free embedding whose domain of validity is known in advance.

翻译：我们研究多变量时间序列的无训练固定长度描述符，不仅关注此类描述符的性能如何，更追问其何时能够有效工作。我们的研究对象为$D(τ)$，该描述符基于时滞相关矩阵构建，经Marchenko-Pastur阈值截断后仅保留携带信号的特征值，并通过与类质心的余弦相似度进行分类，无需学习任何参数。本文的核心贡献并非描述符本身，而是一套可证伪的适用性判据。基于平稳高斯VAR(1)模型，我们论证：当信号近似平稳且类别信息存在于跨通道时间耦合（而非边缘单通道功率）时，$D(τ)$能够实现两类分离。我们以半形式化方式推导出三个推论：区分性条件、静态（$τ=0$）协方差退化为随机水平的原因，以及平稳但基于功率判别范式为何会致使描述符失效。该判据具有可操作性：包含两部分的预检测试——增强型Dickey-Fuller平稳性检验与功率基线饱和检验——可在任何训练前预测适用性。我们在混合数据集上验证了这两个组成部分。在满足判据的四种范式（Sleep-EDF、BCI-IV-2a、MIT-BIH、ESC-50）上，该描述符以极低计算成本与强基线方法竞争，在单CPU线程下对Sleep-EDF数据集进行20受试者留一法交叉验证时达到$88.5\pm4.5\%$的准确率。而在违反判据的三种情况中——非平稳ERP、以及属于功率判别范式的金融波动性与可穿戴压力数据——该描述符的失效模式与预检预测完全一致，这些负例结果更具信息价值。我们明确指出，$D(τ)$并非最优表征，其价值在于提供一种紧凑且无训练的嵌入，且其有效域可预先获知。