Function-Valued Causal Influence in Nonlinear Time Series

2026-05-25

AI Summary

Traditional time series causal discovery relies on scalar causal scores, which struggle to capture state-dependent dynamic causal effects in nonlinear systems. This work proposes a Functional Causal Influence (FCI) framework, formally defining this concept for the first time and enabling nonparametric estimation of causal response functions through a neural additive vector autoregressive model combined with Individual Conditional Expectation (ICE) techniques. By moving beyond scalar summaries, the approach overcomes the information bottleneck inherent in conventional scoring methods. It successfully distinguishes causal relationships that exhibit markedly different functional behaviors yet yield identical scalar scores in synthetic data. Furthermore, when applied to empirical research on democratic development, the method uncovers context-specific institutional causal mechanisms that are overlooked by traditional approaches.

Abstract

Causal discovery in time series is increasingly performed using nonlinear machine-learning models, yet the resulting causal relationships are almost always summarized by scalar edge scores. We argue that this practice obscures the true object learned by nonlinear autoregressive models: a state-dependent function whose effect varies across regimes, magnitudes, and contexts. We formalize function-valued causal influence for additive, contribution-decomposable architectures and show that scalar causal scores constitute a severe information bottleneck, conflating between-state variation with within-state residual noise. Using Neural Additive Vector Autoregression as a representative architecture, we introduce a practical framework based on Individual Conditional Expectation for estimating causal response functions directly from trained models. Through controlled synthetic experiments, we demonstrate that edges with indistinguishable scalar scores can exhibit qualitatively different functional behaviors, including monotonic, thresholded, saturating, and sign-changing effects. An applied case study on democratic development further shows that function-valued analysis reveals regime-specific and asymmetric causal structure systematically missed by score-centric approaches.

Problem

• function-valued causal influence
• nonlinear time series
• causal discovery
• scalar edge scores
• state-dependent effects

Innovation

• function-valued causal influence
• nonlinear time series
• Neural Additive Vector Autoregression
• Individual Conditional Expectation
• causal discovery