Sequential Change-Point Detection in State-Space Models

Abstract

The problem of sequential detection of spontaneous changes in equations for unobserved state variables and observations of linear and nonlinear multivariate state-space models is considered. We consider the case of new additive terms and the case of changing coefficients of these equations. The proposed nonparametric method uses the idea of the “moving window” of observations. In Theorem 4.1 the exponential rate of convergence to zero for type 1 error probability (a wrong decision about a change) is proved. In Theorem 4.2 we consider type 2 error probability and the normalized (by the volume N of the moving window) delay time in change-point detection. Asymptotic optimality of the proposed method is proved in Theorem 5.1. Experimental study includes Monte Carlo examples of sequentially detected changes in coefficients of linear and nonlinear state-space models.

Keywords:

• Change-point
• Monte Carlo tests
• Performance measure
• Sequential detection
• State-space model

Subject Classifications:

• 62L10

ACKNOWLEDGMENTS

I am grateful to an Associate Editor and to an anonymous referee for their helpful comments. My special thanks to Professor Nitis Mukhopadhyay for his encouraging remarks and for participants of the session “Change-Point Detection” of IWAP-2010 for a very fruitful discussion of the theme of this article.

Notes

Recommended by N. Mukhopadhyay