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Adaptive sequential segmentation of piecewise stationary time series. (English) Zbl 0584.62155
In this paper, a new effective method for sequential adaptive segmentation is proposed, which is based on parallel application of two sequential parameter estimation procedures. The detection of a parameter change as well as the estimation of the accurate position of a segment boundary is effectively performed by a sequence of suitable generalized likelihood ratio (GLR) tests. Flow charts as well as a block diagram of the algorithm are presented.
The adjustment of the three control parameters of the procedure (the AR model order, a threshold for the GLR test, and the length of a ”test window”) is discussed with respect to various performance features.
The results of simulation experiments are presented which demonstrate the good detection properties of the algorithm and in particular an excellent ability to allocate the segment boundaries even within a sequence of short segments. As an application to biomedical signals, the analysis of human electroencephalograms (EEG) is considered and an example is shown.

MSC:
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62-04 Software, source code, etc. for problems pertaining to statistics
62L12 Sequential estimation
65C99 Probabilistic methods, stochastic differential equations
62M07 Non-Markovian processes: hypothesis testing
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[1] Bodenstein, G.; Praetorius, H.M., Feature extraction from the electroencephalogram by adaptive segmentation, (), 642-652, (5)
[2] Brandt, A.v., An entropy distance measure for segmentation and clustering of time series with application to EEG signals, (), 981-984
[3] Jansen, B.H.; Hasman, A.; Lenten, R., Piecewise analysis of EEGs using AR-modeling and clustering, Comput. and biomed. res., 14, 168-178, (1981)
[4] De Souza, P.; Thomson, P.J., LPC distance measures and statistical tests with particular reference to the likelihood ratio, IEEE trans. acoust. speech signal process., ASSP-30, 2, 304-315, (Apr. 1982)
[5] Makhoul, J., Linear prediction: A tutorial review, (), 561-580
[6] Porat, B.; Friedlander, B.; Morf, M., Square-root covariance ladder algorithms, IEEE trans. automat. control., AC-27, 4, 813-829, (1982) · Zbl 0492.93072
[7] Michael, D.; Houchin, J., Automatic EEG analysis: A segmentation procedure based on the autocorrelation function, Electroenceph. clin. neurophysiol., 46, 232-235, (1979)
[8] Akaike, H., A new look at the statistical model identification, IEEE trans. automat. control, AC-19, 6, 716-723, (1974) · Zbl 0314.62039
[9] Basseville, M., Edge detection using sequential methods for change in level. part II: sequential detection of change in Mean, IEEE trans. acoust. speech signal process., ASSP-29, 1, 32-50, (Feb. 1981)
[10] Gibson, J.D., Adaptive prediction in speech differential encoding systems, (), 488-525
[11] Rissanen, J., Modelling by shortest data description, Automatica, 14, 465-471, (1978) · Zbl 0418.93079
[12] Sanderson, A.C.; Segen, J.; Richey, E., Hierarchical modeling of EEG signals, IEEE trans. pattern anal. machine int., PAMI-2, 5, 405-415, (Sept. 1980)
[13] Barlow, J.S.; Creutzfeld, O.D.; Michael, D.; Houchin, J.; Epelbaum, H., Automatic adaptive segmentation of clinical eegs, Electroenceph. clin. neurophysiol., 51, 512-525, (1981)
[14] Brandt, A.v., Detecting and estimating parameter jumps using ladder algorithms and likelihood ratio tests, () · Zbl 0552.93068
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