June 2024 A high-dimensional approach to measure connectivity in the financial sector
Sumanta Basu, Sreyoshi Das, George Michailidis, Amiyatosh Purnanandam
Author Affiliations +
Ann. Appl. Stat. 18(2): 922-945 (June 2024). DOI: 10.1214/22-AOAS1702


Data-driven network models to measure systemic risk in the financial sector and identify “too-connected-to-fail” institutions are becoming increasingly common in financial applications. Existing statistical methods for building such networks either take a pairwise approach of fitting many bivariate models or a system-wide approach of fitting penalized regression models. The former strategy is prone to large false positive selection, while the latter suffers from shrinkage bias and lack of formal inference machinery. These issues are accentuated in small sample, low signal-to-noise settings common in financial data. Building up on recent advances in high-dimensional inference, we propose debiased lasso Penalized Vector Autoregression (DLVAR), a method for building financial networks that addresses these limitations. Our empirical analysis highlights the importance of debiasing in a way that increases power of the algorithm in finite samples. We also provide formal inference guarantees of Granger causality tests in high-dimension to justify our method. We apply DLVAR to the stock returns of U.S. large financial institutions covering the period 1990–2021 and illustrate its usefulness in detecting systemically risky periods and institutions, especially during the Great Financial Crisis of 2008–2009 and the most recent Covid-19 related market shock.

Funding Statement

SB was supported in part by NSF Grants DMS-1812128, DMS-2210675, DMS-2239102, and NIH Grants R01GM135926, R21NS120227.
GM was supported in part by NSF Grants IIS-1632730, DMS-1830175 and DMS-1821220.


We would like to thank Viral Acharya, Francis Diebold, Robert Engle, Giampaolo Gabbi, Andreas Hagemann, Indrajit Mitra, Stefan Nagel, Uday Rajan, Toni Whited and seminar participants at the 2017 Conference on “Banks, Systemic Risk, Measurement and Mitigation” at Sapienza University, the Bank of International Settlement, the Cornell ORIE Colloquium, the DSMM conference in San Francisco, the FDIC, the International Indian Statistical Association (IISA) Conference, the International Society for Non-Parametric Statistics (ISNPS), the NBER Summer Institute (2017), the Office of Financial Research (OFR), the University of Michigan Finance brown bag and the Michigan Finance-Economics conference for helpful comments on the paper. All remaining errors are our own.


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Sumanta Basu. Sreyoshi Das. George Michailidis. Amiyatosh Purnanandam. "A high-dimensional approach to measure connectivity in the financial sector." Ann. Appl. Stat. 18 (2) 922 - 945, June 2024. https://doi.org/10.1214/22-AOAS1702


Received: 1 September 2020; Revised: 1 December 2021; Published: June 2024
First available in Project Euclid: 5 April 2024

Digital Object Identifier: 10.1214/22-AOAS1702

Keywords: debiased Lasso , systemic risk , vector autoregression

Rights: Copyright © 2024 Institute of Mathematical Statistics


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Vol.18 • No. 2 • June 2024
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