Hierarchical Representations for Evolving Acyclic Vector Autoregressions (HEAVe)

TL;DR

This paper introduces a flexible evolutionary method for modeling acyclic vector autoregressive processes, enabling hierarchical causal network analysis in time series data with minimal loss of predictive accuracy.

Contribution

It presents a novel hierarchical representation and an evolutionary fitting approach for acyclic VAR models, improving interpretability and computational efficiency.

Findings

Retains most predictive accuracy compared to unconstrained models

Outperforms permutation-based alternatives in simulations

Generates meaningful hierarchical causal networks in cryptocurrency data

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.