# Beyond Coefficients: Forecast-Necessity Testing for Interpretable Causal Discovery in Nonlinear Time-Series Models

arXiv: https://arxiv.org/abs/2604.18751 · HTML: https://mlsanity.com/paper/2604.18751/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 30 of its 65 references that are in the map.
- First posted on arXiv 20 Apr 2026.

## Builds on (most cited first, 30 of 30)

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- [L2C2: Locally Lipschitz Continuous Constraint towards Stable and Smooth Reinforcement Learning](https://mlsanity.com/paper/2202.07152/) (2022)
- [Learning Robust Policy against Disturbance in Transition Dynamics via State-Conservative Policy Optimization](https://mlsanity.com/paper/2112.10513/) (2021)
- [Lipschitz Bounds and Provably Robust Training by Laplacian Smoothing](https://mlsanity.com/paper/2006.03712/) (2020)
- [Robust Deep Reinforcement Learning Through Adversarial Attacks and Training : A Survey](https://mlsanity.com/paper/2403.00420/) (2024)
- [Robust Reinforcement Learning in Continuous Control Tasks with Uncertainty Set Regularization](https://mlsanity.com/paper/2207.02016/) (2022)
- [A Transition-Aware Method for the Simulation of Compliant Contact with Regularized Friction](https://mlsanity.com/paper/1909.05700/) (2019)
- [Interval Observer Synthesis for Locally Lipschitz Nonlinear Dynamical Systems via Mixed-Monotone Decompositions](https://mlsanity.com/paper/2202.11689/) (2022)

## Abstract (arXiv)

Nonlinear machine-learning models are increasingly used to discover causal relationships in time-series data, yet the interpretation of their outputs remains poorly understood. In particular, causal scores produced by regularized neural autoregressive models are often treated as analogues of regression coefficients, leading to misleading claims of statistical significance. In this paper, we argue that causal relevance in nonlinear time-series models should be evaluated through forecast necessity rather than coefficient magnitude, and we present a practical evaluation procedure for doing so. We present an interpretable evaluation framework based on systematic edge ablation and forecast comparison, which tests whether a candidate causal relationship is required for accurate prediction. Using Neural Additive Vector Autoregression as a case study model, we apply this framework to a real-world case study of democratic development, modeled as a multivariate time series of panel data - democracy indicators across 139 countries. We show that relationships with similar causal scores can differ dramatically in their predictive necessity due to redundancy, temporal persistence, and regime-specific effects. Our results demonstrate how forecast-necessity testing supports more reliable causal reasoning in applied AI systems and provides practical guidance for interpreting nonlinear time-series models in high-stakes domains.