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Simultaneous Clustered Orthogonalization

Bastien Buchwalter, Francis X. Diebold, Kamil Yilmaz

arXiv 10 Sep 2026 · Econometrics

arXiv:2609.12280 · PDF · Extracted main text

Abstract

Identification in vector autoregressions involves two distinct choices: how extensively to orthogonalize shocks and whether orthogonality is imposed sequentially or simultaneously. Generalized identification imposes no orthogonality; Sims (1980} imposes full orthogonality sequentially; Francis et al. (2026) impose full orthogonality simultaneously; and Buchwalter et al. (2026a) provide clustered partial orthogonalization sequentially. We fill the remaining case by developing simultaneous clustered orthogonalization (SCO). SCO preserves contemporaneous dependence within economically meaningful clusters while imposing orthogonality across clusters jointly, thereby eliminating dependence on cluster ordering. We formulate the associated correlation-maximizing identification problem and show that, in correlation space, it reduces to a quadratic matrix equation. This yields a closed-form solution, and we prove that the associated identification matrix is the unique global maximizer. SCO is order- and scale-invariant and nests generalized identification and full simultaneous orthogonalization as special cases, yielding a flexible family of structural decompositions indexed by the number and composition of clusters.

Citation extraction

11
references
42
in-text mentions
11
distinct cited
4
self-citations
5,158
main-text words

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Most heavily cited references

The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.

ReferenceIntensityMentionsSectionsMain text
1Francis, N., P. R. Hansen, and C. Tong (2026) Principled identification of structural dynamic models1.000127100%
2Buchwalter, B., F. X. Diebold, and K. Yilmaz (2026) Clustered network connectedness: A new measurement framework with application to global equity markets self1.000105100%
3Koop, G., M. H. Pesaran, and S. M. Potter (1996) Impulse response analysis in nonlinear multivariate models1.00054100%
4Pesaran, M. H. and Y. Shin (1998) Generalized impulse response analysis in linear multivariate models1.00054100%
5Sims, C. A (1980) Macroeconomics and reality0.73732100%
6Buchwalter, B., F. X. Diebold, and K. Yilmaz (2026) Scalable clustered network connectedness with control variables: Theory and application to global banking self0.64422100%
7Diebold, F. X. and K. Yilmaz (2012) Better to give than to receive: Predictive directional measurement of volatility spillovers self0.40511100%
8Diebold, F. X. and K. Ylmaz (2014) On the network topology of variance decompositions: Measuring the connectedness of financial firms self0.40511100%
9Forbes, K. J. and R. Rigobon (2002) No contagion, only interdependence: measuring stock market comovements0.40511100%
10Karush, W (1939) Minima of functions of several variables with inequalities as side conditions0.40511100%

Showing the top 10 of 11 scored citations.