Order-Constrained Spectral Causality for Multivariate Time Series
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866914460520677376 |
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| author | Dominguez, Alejandro Rodriguez |
| author_facet | Dominguez, Alejandro Rodriguez |
| contents | We introduce an operator-theoretic framework for analyzing directional dependence in multivariate time series based on order-constrained spectral non-invariance. Directional influence is defined as the sensitivity of second-order dependence operators to admissible, order-preserving temporal deformations of a designated source component, summarized through orthogonally invariant spectral functionals. We show that the resulting supremum--infimum dispersion functional is the unique diagnostic within this class satisfying order consistency, orthogonal invariance, Loewner monotonicity, second-order sufficiency, and continuity, and that classical Granger causality, directed coherence, and Geweke frequency-domain causality arise as special cases under appropriate restrictions. An information-theoretic impossibility result establishes that entrywise-stable edge-based tests require quadratic sample size scaling in distributed (non-sparse) regimes, whereas spectral tests detect at the optimal linear scale. We establish uniform consistency and valid shift-based randomization inference under weak dependence. Simulations confirm correct size and strong power across distributed and nonlinear alternatives, and an empirical application illustrates system-level directional causal structure in financial markets. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_01216 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Order-Constrained Spectral Causality for Multivariate Time Series Dominguez, Alejandro Rodriguez Applications Statistics Theory Statistical Finance 62M10, 62H25, 60G10, 62G09, 47A10 G.3; G.1.6; I.5.1 We introduce an operator-theoretic framework for analyzing directional dependence in multivariate time series based on order-constrained spectral non-invariance. Directional influence is defined as the sensitivity of second-order dependence operators to admissible, order-preserving temporal deformations of a designated source component, summarized through orthogonally invariant spectral functionals. We show that the resulting supremum--infimum dispersion functional is the unique diagnostic within this class satisfying order consistency, orthogonal invariance, Loewner monotonicity, second-order sufficiency, and continuity, and that classical Granger causality, directed coherence, and Geweke frequency-domain causality arise as special cases under appropriate restrictions. An information-theoretic impossibility result establishes that entrywise-stable edge-based tests require quadratic sample size scaling in distributed (non-sparse) regimes, whereas spectral tests detect at the optimal linear scale. We establish uniform consistency and valid shift-based randomization inference under weak dependence. Simulations confirm correct size and strong power across distributed and nonlinear alternatives, and an empirical application illustrates system-level directional causal structure in financial markets. |
| title | Order-Constrained Spectral Causality for Multivariate Time Series |
| topic | Applications Statistics Theory Statistical Finance 62M10, 62H25, 60G10, 62G09, 47A10 G.3; G.1.6; I.5.1 |
| url | https://arxiv.org/abs/2601.01216 |