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The Impossible Trinity of Time-Series Validation: A Conservation Law among Training Sufficiency, Test Coverage, and Temporal Causality

arXiv · AI, language, vision and robotics · article · Sep 2, 2026 · UTC

Validating a model on a time series asks for three things at once: each training run should use most of the sample (sufficiency), the test sets should together cover most of the sample (coverage), and training data should come before test data (causality). We prove that the three cannot be had together and price each one. Let $α$ be the smallest training fraction over folds, $β$ the fraction of the sample covered by tests, $Λ$ the fraction of the sample used as training data from the future of a test point, and $δ$ the distance from a test point to the nearest training point in its future. Eve

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