Function-Valued Causal Influence in Nonlinear Time Series
For researchers using nonlinear models for causal discovery in time series, this work highlights a fundamental limitation of scalar summaries and provides a practical method to recover richer functional insights.
The paper argues that scalar causal scores in nonlinear time series models obscure state-dependent functional effects, and introduces a framework using Individual Conditional Expectation to estimate causal response functions. Experiments show that edges with identical scalar scores can have qualitatively different functional behaviors, and a case study on democratic development reveals regime-specific causal structure missed by scalar approaches.
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.