# zbMATH — the first resource for mathematics

A method of detecting changes in the behaviour of locally stationary sequences. (English) Zbl 0868.62070
Summary: A method for the detection of abrupt changes in the course of a locally stationary sequence is proposed. The method is based on a suitable approximation of an observed sequence by autoregressive models that are compared by means of a similarity measure derived from the asymptotic $$I$$-divergence rate. The method is illustrated by several numerical results.

##### MSC:
 62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH) 62B10 Statistical aspects of information-theoretic topics 62L99 Sequential statistical methods
Full Text:
##### References:
 [1] R. R. Bahadur: Some Limits Theorem in Statistics: Regional Conference Series in Appl. Math. SIAM Pubs., Philadelphia 1971. [2] M. Basseville, A. Benveniste: Sequential detection of abrupt changes in spectral characteristics of digital signals. IEEE Trans. Inform. Theory IT-29 (1983), 5, 709-724. · Zbl 0511.94008 · doi:10.1109/TIT.1983.1056737 [3] M. Basseville, A. Benveniste (eds.): Detection of Abrupt Changes in Signals and Dynamic Systems. (Lecture Notes in Control and Inform. Sci. 77). Springer, Berlin 1986. · Zbl 0578.93056 [4] V. Grenander, M. Rossenblatt: Statistical Analysis of Stationary Time Series. J. Wiley, New York 1957. [5] N. Kligiene, L. A. Telksnys: Methods of detecting instants of change of random process properties. Automat. Remote Control 44 (1983), 1241-1283. · Zbl 0541.93063 [6] H. Kiinsch: Thermodynamics and statistical analysis of Gaussian random fields. Z. Wahrschein. verw. Gebiete 55 (1981), 407-421. · Zbl 0458.60053 [7] J. Michalek: Yule-Walker estimates and asymptotic I-divergence rate. Problems Control Inform. Theory 19 (1990), 5-6, 387-398. · Zbl 0744.62126 [8] I. V. Nikoforov: Sequential Detection of Abrupt Changes in Time Series Properties. Nauka, Moscow 1983 [9] I. Vajda: Theory of Statistical Inference and Information. Kluwer, Dordrecht, Boston 1989. · Zbl 0711.62002 [10] I. Vajda: Distances and discrimination rates of stochastic processes. Stochastic Process. Appl. 3 (1990), 47-57. · Zbl 0701.62084 · doi:10.1016/0304-4149(90)90121-8 [11] A. S. Willsky: A survey of design methods for failure detection in dynamic systems. Automatica 12 (1976), 601-611. · Zbl 0345.93067 · doi:10.1016/0005-1098(76)90041-8
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.