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Re-examining Granger Causality from Causal Bayesian Networks Perspective

S. A. Adedayo

TL;DR

This paper tackles the criticism that Granger causality is merely predictive by reinterpreting GC through Reichenbach's Common Cause Principles and Causal Bayesian Networks. It proposes a causal GC (c-GC) algorithm that takes the conjunction of unconditioned BVGC and conditioned MVGC results, under causal sufficiency and faithfulness, to infer true causal links in time-series data. The authors validate the approach with autoregressive simulations, showing that the inferred connectivity closely matches the ground-truth network and can reveal cycles, while noting that latent confounders remain a challenge. Overall, the work provides a principled framework to derive causal inferences from GC-like tests and demonstrates practical utility in recovering causal structure from complex time-series data.

Abstract

Characterizing cause-effect relationships in complex systems could be critical to understanding these systems. For many, Granger causality (GC) remains a computational tool of choice to identify causal relations in time series data. Like other causal discovery tools, GC has limitations and has been criticized as a non-causal framework. Here, we addressed one of the recurring criticisms of GC by endowing it with proper causal interpretation. This was achieved by analyzing GC from Reichenbach's Common Cause Principles (RCCPs) and causal Bayesian networks (CBNs) lenses. We showed theoretically and graphically that this reformulation endowed GC with a proper causal interpretation under certain assumptions and achieved satisfactory results on simulation.

Re-examining Granger Causality from Causal Bayesian Networks Perspective

TL;DR

This paper tackles the criticism that Granger causality is merely predictive by reinterpreting GC through Reichenbach's Common Cause Principles and Causal Bayesian Networks. It proposes a causal GC (c-GC) algorithm that takes the conjunction of unconditioned BVGC and conditioned MVGC results, under causal sufficiency and faithfulness, to infer true causal links in time-series data. The authors validate the approach with autoregressive simulations, showing that the inferred connectivity closely matches the ground-truth network and can reveal cycles, while noting that latent confounders remain a challenge. Overall, the work provides a principled framework to derive causal inferences from GC-like tests and demonstrates practical utility in recovering causal structure from complex time-series data.

Abstract

Characterizing cause-effect relationships in complex systems could be critical to understanding these systems. For many, Granger causality (GC) remains a computational tool of choice to identify causal relations in time series data. Like other causal discovery tools, GC has limitations and has been criticized as a non-causal framework. Here, we addressed one of the recurring criticisms of GC by endowing it with proper causal interpretation. This was achieved by analyzing GC from Reichenbach's Common Cause Principles (RCCPs) and causal Bayesian networks (CBNs) lenses. We showed theoretically and graphically that this reformulation endowed GC with a proper causal interpretation under certain assumptions and achieved satisfactory results on simulation.
Paper Structure (9 sections, 16 equations, 3 figures, 1 table)

This paper contains 9 sections, 16 equations, 3 figures, 1 table.

Table of Contents

  1. Introduction
  2. Background
  3. Granger Causality
  4. Reichenbach's Common Cause Principles
  5. Causal Bayesian Networks (CBNs)
  6. Our Solution
  7. The Algorithm
  8. Experiment
  9. Conclusions

Figures (3)

  • Figure 1: GC interpretation in CBN as conditional (in)dependence test. Figure \ref{['fig:non_conf']} depicts conventional GC using the pasts of $X_{t-1}^{i} (i.e. \tau = 1$ in this analogy) and $X_{t}^{j}$, both marked green to depict pairs of interest and dashed green arrow showing the dependence test. This, in CBN, as shown in Figure \ref{['fig:CBN']}, is interpreted as a conditional (in)dependence test by conditioning on the pasts of both $X_{t-1}^{i}$ and $X_{t}^{j}$. The red-shaded states are the states in the conditioning sets.
  • Figure 2: Simulated data
  • Figure 3: Side by side view of ground truth matrix A and inferred matric $\hat{A}$