We introduce an operator-theoretic framework for causal analysis in multivariate time series based on order-constrained spectral non-invariance. Directional influence is defined as sensitivity of second-order dependence operators to admissible, order-preserving temporal deformations of a designated source component, yielding an intrinsically multivariate causal notion summarized through orthogonally invariant spectral functionals. Under linear Gaussian assumptions, the criterion coincides with linear Granger causality, while beyond this regime it captures collective and nonlinear directional dependence not reflected in pairwise predictability. We establish existence, uniform consistency, and valid inference for the resulting non-smooth supremum--infimum statistics using shift-based randomization that exploits order-induced group invariance, yielding finite-sample exactness under exact invariance and asymptotic validity under weak dependence without parametric assumptions. Simulations demonstrate correct size and strong power against distributed and bulk-dominated alternatives, including nonlinear dependence missed by linear Granger tests with appropriate feature embeddings. An empirical application to a high-dimensional panel of daily financial return series spanning major asset classes illustrates system-level causal monitoring in practice. Directional organization is episodic and stress-dependent, causal propagation strengthens while remaining multi-channel, dominant causal hubs reallocate rapidly, and statistically robust transmission channels are sparse and horizon-heterogeneous even when aggregate lead--lag asymmetry is weak. The framework provides a scalable and interpretable complement to correlation-, factor-, and pairwise Granger-style analyses for complex systems.

翻译：我们提出了一种基于序约束谱非不变性的多元时间序列因果分析算子理论框架。方向性影响被定义为二阶依赖算子对指定源分量在允许的保序时间形变下的敏感性，从而产生一种本质上的多元因果概念，并通过正交不变谱泛函进行概括。在线性高斯假设下，该准则与线性格兰杰因果性一致，而在此范围之外，它捕捉了成对可预测性未能反映的集体和非线性方向依赖性。我们利用序诱导的群不变性，通过基于平移的随机化方法，为所得的非光滑上确界-下确界统计量建立了存在性、一致一致性和有效推断，在精确不变性下具有有限样本精确性，在弱依赖性下无需参数假设即具有渐近有效性。仿真实验表明，该方法具有正确的检验水平，并对分布式和主体主导的备择假设（包括通过适当特征嵌入被线性格兰杰检验遗漏的非线性依赖性）表现出较强的检验功效。一项针对涵盖主要资产类别的日度金融收益率高维面板数据的实证应用，展示了系统级因果监测的实践。方向性组织具有间歇性和压力依赖性，因果传播在保持多通道的同时增强，主导的因果枢纽快速重新分配，且即使在总体的领先-滞后不对称性较弱时，统计上稳健的传输通道也是稀疏且具有时域异质性的。该框架为复杂系统的相关性分析、因子分析以及成对格兰杰式分析提供了一个可扩展且可解释的补充。