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Model Selection Criteria in Multivariate Models with Multiple Structural Changes

Author

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  • Eiji Kurozumi
  • Purevdorj Tuvaandorj

Abstract

This paper considers the issue of selecting the number of regressors and the number of structural breaks in multivariate regression models in the possible presence of mul- tiple structural changes. We develop a modified Akaike's information criterion (AIC), a modified Mallows' Cp criterion and a modified Bayesian information criterion (BIC). The penalty terms in these criteria are shown to be different from the usual terms. We prove that the modified BIC consistently selects the regressors and the number of breaks whereas the modified AIC and the modified Cp criterion tend to overly choose them with positive probability. The finite sample performance of these criteria is investigated through Monte Carlo simulations and it turns out that our modification is successful in comparison to the classical model selection criteria and the sequential testing procedure with the robust method.

Suggested Citation

  • Eiji Kurozumi & Purevdorj Tuvaandorj, 2010. "Model Selection Criteria in Multivariate Models with Multiple Structural Changes," Global COE Hi-Stat Discussion Paper Series gd10-144, Institute of Economic Research, Hitotsubashi University.
    • Handle: RePEc:hst:ghsdps:gd10-144
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    Cited by:

    1. Harris, David & Leybourne, Stephen J. & Taylor, A.M. Robert, 2016. "Tests of the co-integration rank in VAR models in the presence of a possible break in trend at an unknown point," Journal of Econometrics, Elsevier, vol. 192(2), pages 451-467.
    2. Eo, Yunjong & Morley, James C., 2008. "Likelihood-Based Confidence Sets for the Timing of Structural Breaks," MPRA Paper 10372, University Library of Munich, Germany.
    3. Gavard, Claire & Kirat, Djamel, 2020. "Short-term impacts of carbon offsetting on emissions trading schemes: Empirical insights from the EU experience," ZEW Discussion Papers 20-058, ZEW - Leibniz Centre for European Economic Research.
    4. Nakaota, Hiroshi & Fukuta, Yuichi, 2013. "The leading indicator property of the term spread and the monetary policy factors in Japan," Japan and the World Economy, Elsevier, vol. 28(C), pages 85-98.
    5. Yunjong Eo & James Morley, 2015. "Likelihood‐ratio‐based confidence sets for the timing of structural breaks," Quantitative Economics, Econometric Society, vol. 6(2), pages 463-497, July.
    6. Yaein Baek, 2018. "Estimation of a Structural Break Point in Linear Regression Models," Papers 1811.03720, arXiv.org, revised Jun 2020.
    7. Mikihito Nishi, 2024. "Estimating Time-Varying Parameters of Various Smoothness in Linear Models via Kernel Regression," Papers 2406.14046, arXiv.org, revised Jan 2026.
    8. Oka, Tatsushi & Perron, Pierre, 2018. "Testing for common breaks in a multiple equations system," Journal of Econometrics, Elsevier, vol. 204(1), pages 66-85.
    9. Pierre Perron & Yohei Yamamoto & Jing Zhou, 2020. "Testing jointly for structural changes in the error variance and coefficients of a linear regression model," Quantitative Economics, Econometric Society, vol. 11(3), pages 1019-1057, July.
    10. KUROZUMI, Eiji & 黒住, 英司, 2016. "Monitoring Parameter Constancy with Endogenous Regressors," Discussion Papers 2016-01, Graduate School of Economics, Hitotsubashi University.
    11. Hiroshi Nakaota & Yuichi Fukuta, 2013. "The Leading Indicator Property of the Term Spread and the Monetary Policy Factors in Japan," Discussion Papers in Economics and Business 13-09, Osaka University, Graduate School of Economics, revised Jul 2013.
    12. Ibrahim Ahamada & Jose Luis Diaz Sanchez, 2013. "A Retrospective Analysis of the House Prices Macro-Relationship in the United States," International Journal of Central Banking, International Journal of Central Banking, vol. 9(4), pages 153-174, December.
    13. Alessandro Casini & Pierre Perron, 2018. "Structural Breaks in Time Series," Papers 1805.03807, arXiv.org.
    14. Otilia Boldea & Alastair R. Hall, 2025. "Testing for multiple change-points in macroeconometrics: an empirical guide and recent developments," Papers 2507.22204, arXiv.org.
    15. Huang, Chuangxia & Cai, Yaqian & Yang, Xiaoguang & Deng, Yanchen & Yang, Xin, 2023. "Laplacian-energy-like measure: Does it improve the Cross-Sectional Absolute Deviation herding model?," Economic Modelling, Elsevier, vol. 127(C).
    16. Jose Barrales-Ruiz & Gyeongho Kim & Ivan Mendieta-Munoz, 2025. "Time-varying endogenous productivity growth dynamics," Working Papers 2515, New School for Social Research, Department of Economics.
    17. Hiroshi Nakaota & Yuichi Fukuta, 2013. "The Leading Indicator Property of the Term Spread and the Monetary Policy Factors in Japan," Discussion Papers in Economics and Business 13-09-Rev, Osaka University, Graduate School of Economics.
    18. Jan Mutl & Leopold Sögner, 2019. "Parameter estimation and inference with spatial lags and cointegration," Econometric Reviews, Taylor & Francis Journals, vol. 38(6), pages 597-635, July.
    19. Djamel KIRAT & Claire GAVARD, 2020. "Short-term impacts of carbon offsetting on emissions trading schemes: empirical insights from the EU experience," LEO Working Papers / DR LEO 2821, Orleans Economics Laboratory / Laboratoire d'Economie d'Orleans (LEO), University of Orleans.
    20. Takuya Maruyama & Kazutake Taguchi, 2021. "Increased motor vehicle crashes following the 2016 Kumamoto earthquake, Japan: an interrupted time series analysis of property damage crashes," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 108(2), pages 1877-1899, September.
    21. Alaa Abi Morshed & Elena Andreou & Otilia Boldea, 2018. "Structural Break Tests Robust to Regression Misspecification," Econometrics, MDPI, vol. 6(2), pages 1-39, May.
    22. Harris, David & Kew, Hsein & Taylor, A.M. Robert, 2020. "Level shift estimation in the presence of non-stationary volatility with an application to the unit root testing problem," Journal of Econometrics, Elsevier, vol. 219(2), pages 354-388.

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    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models

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