Non-parametric Causal Discovery for EU Allowances Returns Through the Information Imbalance

Paper: arXiv 2508.15667

Authors: Cristiano Salvagnin, Vittorio del Tatto, Maria Elena De Giuli, Antonietta Mira, Aldo Glielmo

Abstract

We propose to use a recently introduced non-parametric tool named Differentiable Information Imbalance (DII) to identify variables that are causally related – potentially through non-linear relationships – to the financial returns of the European Union Allowances (EUAs) within the EU Emissions Trading System (EU ETS). We examine data from January 2013 to April 2024 and compare the DII approach with multivariate Granger causality, a well-known linear approach based on VAR models. We find significant overlap among the causal variables identified by linear and non-linear methods, such as the coal futures prices and the IBEX35 index. We also find important differences between the two causal sets identified. On two synthetic datasets, we show how these differences could originate from limitations of the linear methodology.

Complexity vs Empirical Score

• Math Complexity: 7.5/10
• Empirical Rigor: 6.0/10
• Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper employs advanced non-parametric and information-theoretic methods (DII, Transfer Entropy) with explicit mathematical formulations, indicating high mathematical complexity. It also demonstrates empirical rigor through extensive backtesting on synthetic and real-world financial data (EU ETS) with comparative analyses and time-series validation.

Research Flowchart

  flowchart TD
  A["Research Goal: Identify Causal Drivers<br>of EU Allowances Returns"] --> B["Data: EU ETS & Financial Data<br>Jan 2013 - Apr 2024"]
  B --> C{"Methodology Comparison"}
  
  C --> D["Non-parametric Approach<br>Differentiable Information Imbalance<br>Detects non-linear causality"]
  C --> E["Linear Approach<br>Multivariate Granger Causality<br>VAR models"]
  
  D --> F["Computational Process"]
  E --> F
  
  subgraph F ["Analysis & Validation"]
      F1["Real Data Application"]
      F2["Synthetic Data Testing"]
  end
  
  F --> G{"Key Findings & Outcomes"}
  
  G --> H["Overlap: Coal Futures, IBEX35<br>Causally significant in both methods"]
  G --> I["Critical Differences Found<br>Linear methods miss complex non-linear relationships"]
  G --> J["Validation via Synthetics<br>Confirmed linear limitations"]

Cited References (163)

1. Directive 2003/87/EC of the European Parliament and of the Council establishing a scheme for greenhouse gas emission allowance trading within the Community and amending Council Directive 96/61/EC (2003) — link
2. Multivariate Granger causality and generalized variance (2010) — link
3. Towards a robust approach to infer causality in molecular systems satisfying detailed balance (2025) — link
4. Measuring Information Transfer (2000) — link
5. Transfer entropy analysis of the stock market (2005)
6. Speculative Influence Network during financial bubbles: application to Chinese stock markets (2018) — link
7. Effective Transfer Entropy in Credit Markets (2022)
8. Detecting causality in complex ecosystems (2012) — link

1 of 163 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.