On Segmentation of Time Series.
ILLINOIS UNIV AT CHICAGO CIRCLE DEPT OF MATHEMATICS
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The problem of partitioning a time-series into segments is considered. The segments fall into classes, which may correspond to phases of a cycle recession, recovery, expansion in the business cycle or to portions of a signal obtained by scanning backgroundclutter, target, backgroundclutter again, another target, etc. or normal tissue, tumor, normal tissue. Parametric families of distributions are considered, a set of parameter values being associated with each class. With each observation is associated an unobservable label, indicating from which class the observation arose. The label process is modeled as a Markov chain. Segmentation algorithms are obtained by applying a method of iterated maximum likelihood to the resulting likelihood function. In this paper special attention is given to the situation in which the observations are conditionally independent, given the labels. A numerical example is given. Choice of the number of classes, using Akaikes automatic model identification criterion AIC, is illustrated. Prediction is considered. Author
- Statistics and Probability