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Penalty selection for multivariate information criteria with change-points

Derive penalty functions for information criteria that ensure consistent selection of the number of structural breaks in multivariate linear regression models with multiple change-points.

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Background

Although BIC-type criteria exist for multivariate models, appropriate penalties guaranteeing consistent break-number selection have not been established for general multivariate change-point settings. This limits reliable automatic selection of the number of breaks in multivariate macroeconomic applications.

References

Once can also consistently estimate the number of change-points via the BIC information criterion in \citeasnoun{Bai:2000}. However, as discussed for univariate models, the penalty may not be strong enough to detect the correct number of breaks in finite samples, and results on the right penalty for multivariate models with change-points are not currently available to the best of our knowledge.

— Testing for multiple change-points in macroeconometrics: an empirical guide and recent developments (2507.22204 - Boldea et al., 29 Jul 2025) in Section 3, Linear multivariate time series models (Multivariate models)