Structurally Regularized Causal Networks for High-Dimensional Financial Time Series: A STIC×PCMCI Framework

This paper proposes a structurally regularized causal network framework, denoted by STIC×PCMCI, for directional transmission identification and network-based signal construction in high-dimensional financial time series. The framework uses PCMCI to identify lagged causal relations under multivariate conditioning, while the Structural Time-series Interaction Coefficient (STIC) measures unconditional structural co-movement among financial nodes. Three fusion mechanisms, namely the Hard, Soft, and Soft-Truncated regularization mechanisms, are developed to impose structural constraints on candidate causal edges. Theoretical properties are established in terms of support contraction, edge-weight compression, weak-edge deletion, and perturbation bounds for network-induced signals. Using daily returns of Shenwan first-level industry indices in the Chinese A-share market from 2014 to 2025, we find that the pure PCMCI network can extract directional information but tends to generate overly dense networks in noisy financial samples, leading to substantial out-of-sample performance decay. In contrast, STIC-based structural constraints reduce network density, suppress weak-edge noise, and improve drawdown control. Among the proposed variants, the Soft-Truncated mechanism achieves the strongest out-of-sample risk-adjusted performance by balancing network sparsification and edge-weight information preservation. Comparisons with correlation networks and pairwise Granger causality networks further show that financial network signals require both structural co-movement information and high-dimensional conditional directionality. The proposed framework therefore provides a more robust and interpretable approach to causal network modeling in financial time series.