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A Unified Approach to Structural Change Tests Based on ML Scores, F Statistics, and OLS Residuals

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  • Achim Zeileis

Abstract

Three classes of structural change tests (or tests for parameter instability) that have been receiving much attention in both the statistics and the econometrics communities but have been developed in rather loosely connected lines of research are unified by embedding them into the framework of generalized M-fluctuation tests (Zeileis and Hornik, 2003). These classes are tests based on maximum likelihood scores (including the Nyblom-Hansen test), on F statistics (sup F, ave F, exp F tests), and on OLS residuals (OLS-based CUSUM and MOSUM tests). We show that (representatives from) these classes are special cases of the generalized M-fluctuation tests, based on the same functional central limit theorem but employing different functionals for capturing excessive fluctuations. After embedding these tests into the same framework and thus understanding the relationship between these procedures for testing in historical samples, it is shown how the tests can also be extended to a monitoring situation. This is achieved by establishing a general M-fluctuation monitoring procedure and then applying the different functionals corresponding to monitoring with ML scores, F statistics, and OLS residuals. In particular, an extension of the sup F test to a monitoring scenario is suggested and illustrated on a real-world data set.

Suggested Citation

  • Achim Zeileis, 2005. "A Unified Approach to Structural Change Tests Based on ML Scores, F Statistics, and OLS Residuals," Econometric Reviews, Taylor & Francis Journals, vol. 24(4), pages 445-466.
  • Handle: RePEc:taf:emetrv:v:24:y:2005:i:4:p:445-466
    DOI: 10.1080/07474930500406053
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    1. Let’s Party!
      by diffuseprior in DiffusePrioR on 2012-06-06 22:51:06

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    Cited by:

    1. Jan J. J. Groen & George Kapetanios & Simon Price, 2013. "Multivariate Methods For Monitoring Structural Change," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 28(2), pages 250-274, March.
    2. Davinson Stev Abril Salcedo & Luis Fernando Melo Velandia & Daniel Parra Amado, 2015. "Heterogeneidad de los Índices de Producción Sectoriales de la Industria Colombiana," BORRADORES DE ECONOMIA 012973, BANCO DE LA REPÚBLICA.
    3. Marjolein Fokkema & Niels Smits & Achim Zeileis & Torsten Hothorn & Henk Kelderman, 2015. "Detecting Treatment-Subgroup Interactions in Clustered Data with Generalized Linear Mixed-Effects Model Trees," Working Papers 2015-10, Faculty of Economics and Statistics, University of Innsbruck.
    4. Makram El-Shagi & Sebastian Giesen, 2013. "Testing for Structural Breaks at Unknown Time: A Steeplechase," Computational Economics, Springer;Society for Computational Economics, vol. 41(1), pages 101-123, January.
    5. Kleiber, Christian, 2016. "Structural change in (economic) time series," Working papers 2016/06, Faculty of Business and Economics - University of Basel.
    6. Yi-Hsuan Lee & Alina Davier, 2013. "Monitoring Scale Scores over Time via Quality Control Charts, Model-Based Approaches, and Time Series Techniques," Psychometrika, Springer;The Psychometric Society, vol. 78(3), pages 557-575, July.
    7. repec:taf:applec:v:49:y:2017:i:2:p:170-187 is not listed on IDEAS
    8. Thomas Windberger & Achim Zeileis, 2011. "Structural Breaks in Inflation Dynamics within the European Monetary Union," Working Papers 2011-12, Faculty of Economics and Statistics, University of Innsbruck.
    9. Jamel Jouini, 2010. "Bootstrap methods for single structural change tests: power versus corrected size and empirical illustration," Statistical Papers, Springer, vol. 51(1), pages 85-109, January.
    10. Martin Wagner & Achim Zeileis, 2012. "Heterogeneity of Regional Growth in the European Union," Working Papers 2012-20, Faculty of Economics and Statistics, University of Innsbruck.
    11. Colin O’hare & Youwei Li, 2017. "Modelling mortality: are we heading in the right direction?," Applied Economics, Taylor & Francis Journals, vol. 49(2), pages 170-187, January.
    12. repec:bla:scjsta:v:44:y:2017:i:4:p:843-865 is not listed on IDEAS
    13. Fried, Roland, 2007. "On the robust detection of edges in time series filtering," Technical Reports 2007,20, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    14. Edgar Merkle & Achim Zeileis, 2013. "Tests of Measurement Invariance Without Subgroups: A Generalization of Classical Methods," Psychometrika, Springer;The Psychometric Society, vol. 78(1), pages 59-82, January.
    15. Achim Zeileis & Torsten Hothorn, 2013. "A toolbox of permutation tests for structural change," Statistical Papers, Springer, vol. 54(4), pages 931-954, November.
    16. Fantazziini, Dean, 2014. "Nowcasting and Forecasting the Monthly Food Stamps Data in the US using Online Search Data," MPRA Paper 59696, University Library of Munich, Germany.
    17. Jan Verbesselt & Achim Zeileis & Martin Herold, 2011. "Near Real-Time Disturbance Detection in Terrestrial Ecosystems Using Satellite Image Time Series: Drought Detection in Somalia," Working Papers 2011-18, Faculty of Economics and Statistics, University of Innsbruck.
    18. Fried, Roland, 2007. "On the robust detection of edges in time series filtering," Computational Statistics & Data Analysis, Elsevier, vol. 52(2), pages 1063-1074, October.
    19. Zeileis, Achim & Shah, Ajay & Patnaik, Ila, 2010. "Testing, monitoring, and dating structural changes in exchange rate regimes," Computational Statistics & Data Analysis, Elsevier, vol. 54(6), pages 1696-1706, June.
    20. Yazgan, M. Ege & Özkan, Harun, 2015. "Detecting structural changes using wavelets," Finance Research Letters, Elsevier, vol. 12(C), pages 23-37.
    21. repec:bla:jtsera:v:38:y:2017:i:5:p:791-805 is not listed on IDEAS
    22. O'Hare, Colin & Li, Youwei, 2014. "Identifying structural breaks in stochastic mortality models," MPRA Paper 62994, University Library of Munich, Germany.
    23. Susan Athey & Julie Tibshirani & Stefan Wager, 2016. "Generalized Random Forests," Papers 1610.01271, arXiv.org, revised Apr 2018.

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