Adaptive sequential segmentation of piecewise stationary time series.

*(English)*Zbl 0584.62155In 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.

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 |

##### Keywords:

piecewise stationary time series; sequential adaptive segmentation; detection of a parameter change; generalized likelihood ratio (GLR) tests; Flow charts; block diagram; AR model order; threshold; test window; simulation experiments; segment boundaries; human electroencephalograms
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\textit{U. Appel} and \textit{A. V. Brandt}, Inf. Sci. 29, 27--56 (1983; Zbl 0584.62155)

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##### References:

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