# ONE MODIFICATION OF THE CUSUM TEST FOR DETECTION EARLY STRUCTURAL CHANGES

### Julia Bondarenko

#### Abstract

Structural shifts in time series can occur as consequences of complex processes, arising in system. An ignorance of such structural changes can cause an associated regression model misspecification. In practice, early detection and response to outbreaks, causing the changes in a process, is highly important. The famous CUSUM test of Brown, Durbin & Evans, has a poor power in detecting the structural breaks in parameters occurring early (and also late) in the sample. In this paper, we propose CUSUM-similar test which, due to the transformation of recursive residuals forces the detection of temporal dependence structure in linear regression model and has a larger power for the early structural breaks. Here our interest centres on the detection of single breaks occurring in parameters of the linear model. Distribution and other probabilistic characteristics of the transformed residuals are provided, the boundaries for the new test are derived. The new test can be considered then as a complement to the standard CUSUM test.

#### References

- Basseville, M. and Nikiforov, I. (1993). Detection of Abrupt Changes - Theory and Application. Prentice Hall, Englewood Cliffs, NJ.
- C.-S. J. Chu, K. H. and Kuan, C.-M. (1995a). Mosum tests for parameter constancy. Biometrika, 82:603-617.
- C.-S. J. Chu, K. H. and Kuan, C.-M. (1995b). The movingestimates test for parameter stability. Econometric Theory, 11:669-720.
- Inder, B. and Hao, K. (1996). A new test for structural change. Empirical Economics, 21:475-482.
- Kraemer, W. and Sonnberg, H. (1986). The Linear Regression Model under Test. Physica-Verlag, Heidelberg.
- Luger, R. (2001). A modified cusum test for orthogonal structural changes. Economic Letters, 73:301-306.
- Proberger, W. and Kraemer, W. (1990). The local power of the cusum and cusum of squares tests. Econometric Theory, 6:335-347.
- Proberger, W. and Kraemer, W. (1992). The cusum test with ols residuals. Econometrica, 60:271-285.
- R. L. Brown, J. D. and Evans, J. M. (1975). Techniques for testing the constancy of regression relationships over time. Journal of Royal Statistical Society B, 27:149- 163.
- Tanizaki, H. (1995). Asymptotically exact confidence intervals of cusum and cusumq tests: a numerical derivations using simulation technique. Communications in Statistics, 24:1019-1036.
- W. Kraemer, W. P. and Alt, R. (1988). Testing for structural change in dynamic models. Econometrica, 56:1355- 1369.
- W. Proberger, W. K. and Alt, R. (1989). A modification of the cusum test in the linear regression model with lagged dependent variables. Empirical Economics, 14:65-75.
- Zeileis, A. (2000). p-values and alternative boundaries for cusum tests. SFB Adaptive Information Systems and Modelling in Economics and Management Science, Working Paper 78.

#### Paper Citation

#### in Harvard Style

Bondarenko J. (2008). **ONE MODIFICATION OF THE CUSUM TEST FOR DETECTION EARLY STRUCTURAL CHANGES** . In *Proceedings of the Fifth International Conference on Informatics in Control, Automation and Robotics - Volume 3: ICINCO,* ISBN 978-989-8111-32-6, pages 18-22. DOI: 10.5220/0001482900180022

#### in Bibtex Style

@conference{icinco08,

author={Julia Bondarenko},

title={ONE MODIFICATION OF THE CUSUM TEST FOR DETECTION EARLY STRUCTURAL CHANGES},

booktitle={Proceedings of the Fifth International Conference on Informatics in Control, Automation and Robotics - Volume 3: ICINCO,},

year={2008},

pages={18-22},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0001482900180022},

isbn={978-989-8111-32-6},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the Fifth International Conference on Informatics in Control, Automation and Robotics - Volume 3: ICINCO,

TI - ONE MODIFICATION OF THE CUSUM TEST FOR DETECTION EARLY STRUCTURAL CHANGES

SN - 978-989-8111-32-6

AU - Bondarenko J.

PY - 2008

SP - 18

EP - 22

DO - 10.5220/0001482900180022