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Uncovering Sparse Financial Networks with Information Criteria

Fu Ouyang, Thomas T. Yang, Wenying Yao

TL;DR

The paper tackles the problem that Diebold–Yilmaz FEVD-based financial networks are densely connected, obscuring key transmission channels. It recasts FEVD as a regression problem and develops an information-criterion framework that consistently recovers the active set of spillover channels, with an extension to Generalized FEVDs and a data-driven tuning rule via pseudo-out-of-sample forecasts. Monte Carlo experiments show the method reliably identifies true connections across small and large networks, remains robust to approximate sparsity and heavy-tailed errors, and achieves strong sparsity with minimal loss in explained variance. Empirically, the approach yields sparse, economically interpretable networks for global stock markets, S&P 500 sectors, and commodity volatility, challenging dense Diebold–Yilmaz interpretations and aiding systemic risk monitoring. Overall, the framework provides a transparent, scalable tool for identifying the key channels of financial contagion by balancing model fit and parsimony, with clear guidance on FEVD vs GFEVD depending on the objective.”

Abstract

Empirical measures of financial connectedness based on Forecast Error Variance Decompositions (FEVDs) often yield dense network structures that obscure true transmission channels and complicate the identification of systemic risk. This paper proposes a novel information-criterion-based approach to uncover sparse, economically meaningful financial networks. By reformulating FEVD-based connectedness as a regression problem, we develop a model selection framework that consistently recovers the active set of spillover channels. We extend this method to generalized FEVDs to accommodate correlated shocks and introduce a data-driven procedure for tuning the penalty parameter using pseudo-out-of-sample forecast performance. Monte Carlo simulations demonstrate the approach's effectiveness with finite samples and its robustness to approximately sparse networks and heavy-tailed errors. Applications to global stock markets, S&P 500 sectoral indices, and commodity futures highlight the prevalence of sparse networks in empirical settings.

Uncovering Sparse Financial Networks with Information Criteria

TL;DR

The paper tackles the problem that Diebold–Yilmaz FEVD-based financial networks are densely connected, obscuring key transmission channels. It recasts FEVD as a regression problem and develops an information-criterion framework that consistently recovers the active set of spillover channels, with an extension to Generalized FEVDs and a data-driven tuning rule via pseudo-out-of-sample forecasts. Monte Carlo experiments show the method reliably identifies true connections across small and large networks, remains robust to approximate sparsity and heavy-tailed errors, and achieves strong sparsity with minimal loss in explained variance. Empirically, the approach yields sparse, economically interpretable networks for global stock markets, S&P 500 sectors, and commodity volatility, challenging dense Diebold–Yilmaz interpretations and aiding systemic risk monitoring. Overall, the framework provides a transparent, scalable tool for identifying the key channels of financial contagion by balancing model fit and parsimony, with clear guidance on FEVD vs GFEVD depending on the objective.”

Abstract

Empirical measures of financial connectedness based on Forecast Error Variance Decompositions (FEVDs) often yield dense network structures that obscure true transmission channels and complicate the identification of systemic risk. This paper proposes a novel information-criterion-based approach to uncover sparse, economically meaningful financial networks. By reformulating FEVD-based connectedness as a regression problem, we develop a model selection framework that consistently recovers the active set of spillover channels. We extend this method to generalized FEVDs to accommodate correlated shocks and introduce a data-driven procedure for tuning the penalty parameter using pseudo-out-of-sample forecast performance. Monte Carlo simulations demonstrate the approach's effectiveness with finite samples and its robustness to approximately sparse networks and heavy-tailed errors. Applications to global stock markets, S&P 500 sectoral indices, and commodity futures highlight the prevalence of sparse networks in empirical settings.
Paper Structure (22 sections, 3 theorems, 62 equations, 5 figures, 8 tables, 2 algorithms)

This paper contains 22 sections, 3 theorems, 62 equations, 5 figures, 8 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. The Regression Perspective
  3. A Regression Interpretation of FEVD
  4. Sparsity in $H$-step-ahead FEVD
  5. Information Criterion
  6. Data-Driven Selection of the Tuning Parameter $\lambda_{T}$
  7. Extension to Generalized FEVD
  8. Monte Carlo Experiments
  9. Small Networks
  10. Large Networks
  11. Approximately Sparse Networks
  12. Heavy-tailed Errors
  13. Empirical Applications
  14. DieboldYilmaz2009 network
  15. S&P 500 Sector Network
  16. ...and 7 more sections

Key Result

Theorem 2.1

Suppose Assumptions A:model--A:A1 hold. Let $\lambda_{T}\rightarrow\infty$ and $\lambda_{T}/T\rightarrow0$ as $T\rightarrow\infty$. Then, the selection procedure eq:IC_k--eq:est_active, based on the information criterion proposed in eq:IC_general, is consistent in the sense that

Figures (5)

  • Figure 1: The distribution of the selected constant $c^\ast$
  • Figure 2: S&P 500 sectoral network
  • Figure B.1: The distribution of the selected constant $c^\ast$ for DGPs L1 and L2 with FEVD
  • Figure B.2: The distribution of the selected constant $c^\ast$ for DGPs H1 and H2 with FEVD
  • Figure B.3: The distribution of the selected constant $c^\ast$ for DGPs H1 and H2 with GFEVD

Theorems & Definitions (3)

  • Theorem 2.1
  • Lemma A.1
  • Lemma A.2