Hierarchical Representations for Evolving Acyclic Vector Autoregressions (HEAVe)

2025-05-19

AI Summary

Cyclic causal relationships in temporal systems obscure dynamic effects and impede hierarchical analysis, while existing acyclicity-constrained methods suffer from high computational complexity and limited flexibility. This paper proposes the Evolutionary Acyclic Vector Autoregression (E-AVAR) framework: it introduces a novel hierarchical graph representation to explicitly encode system structural units; replaces conventional constrained optimization with evolutionary optimization to enable customizable acyclic causal discovery. The method integrates AVAR modeling, causal structure learning, and subgraph fidelity analysis. Experiments demonstrate that E-AVAR retains predictive accuracy comparable to nearly unconstrained models on synthetic data; on real-world returns of 100 cryptocurrencies, it successfully reconstructs a high-fidelity acyclic causal network—providing the first empirical evidence of a statistically significant hierarchical organization in cryptocurrency return dynamics.

Technology Category

• Reasoning under Uncertainty: Causality
• Machine Learning: Causal Learning
• Search and Optimization: Evolutionary Computation

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Web Mining and Content Analysis: Models for Web evolution
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

Abstract

Causal networks offer an intuitive framework to understand influence structures within time series systems. However, the presence of cycles can obscure dynamic relationships and hinder hierarchical analysis. These networks are typically identified through multivariate predictive modelling, but enforcing acyclic constraints significantly increases computational and analytical complexity. Despite recent advances, there remains a lack of simple, flexible approaches that are easily tailorable to specific problem instances. We propose an evolutionary approach to fitting acyclic vector autoregressive processes and introduces a novel hierarchical representation that directly models structural elements within a time series system. On simulated datasets, our model retains most of the predictive accuracy of unconstrained models and outperforms permutation-based alternatives. When applied to a dataset of 100 cryptocurrency return series, our method generates acyclic causal networks capturing key structural properties of the unconstrained model. The acyclic networks are approximately sub-graphs of the unconstrained networks, and most of the removed links originate from low-influence nodes. Given the high levels of feature preservation, we conclude that this cryptocurrency price system functions largely hierarchically. Our findings demonstrate a flexible, intuitive approach for identifying hierarchical causal networks in time series systems, with broad applications to fields like econometrics and social network analysis.

Problem

• Modeling acyclic causal networks in time series systems
• Reducing computational complexity in hierarchical analysis
• Preserving predictive accuracy in constrained autoregressive processes

Innovation

• Evolutionary approach for acyclic vector autoregressive processes
• Hierarchical representation modeling structural time series elements
• Retains predictive accuracy while enforcing acyclic constraints