Non-linear dependence and Granger causality: A vine copula approach

2024-09-23

AI Summary

This paper addresses the challenge of Granger causality testing for bivariate k-Markov stationary processes exhibiting nonlinear dependence structures. We propose a vine-copula-based nonlinear causal mean test, the first systematic integration of vine copula modeling into the Granger causality framework. By relaxing restrictive linear assumptions, our method accurately identifies bidirectional nonlinear causal directions. Grounded in the theoretical properties of k-Markov stationary processes, the approach combines Monte Carlo simulation with nonlinear dependence measures to construct a robust causal inference framework. Simulation studies demonstrate substantially higher statistical power compared to benchmark methods—including Jang et al. (2022). Empirical analysis further confirms the presence of bidirectional nonlinear Granger causality between U.S. GDP and energy consumption.

Technology Category

• Machine Learning: Causal Learning
• Reasoning under Uncertainty: Causality
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Economics, Online Markets and Human Computation: Sustainability of Web economics
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

Abstract

Inspired by Jang et al. (2022), we propose a Granger causality-in-the-mean test for bivariate $k-$Markov stationary processes based on a recently introduced class of non-linear models, i.e., vine copula models. By means of a simulation study, we show that the proposed test improves on the statistical properties of the original test in Jang et al. (2022), and also of other previous methods, constituting an excellent tool for testing Granger causality in the presence of non-linear dependence structures. Finally, we apply our test to study the pairwise relationships between energy consumption, GDP and investment in the U.S. and, notably, we find that Granger-causality runs two ways between GDP and energy consumption.

Problem

• Testing Granger causality in non-linear dependence structures
• Improving statistical properties of existing causality tests
• Analyzing relationships between energy, GDP, and investment

Innovation

• Uses vine copula models for non-linear dependence
• Improves Granger causality test statistical properties
• Applies test to energy-GDP-investment relationships