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Ansgar Steland

Jump-preserving monitoring of dependent time series using pilot estimators

An important problem of the statistical analysis of time series is to detect change-points in the mean structure. Since this problem is aone-dimensional version of the higher dimensional problem of detecting edges in images, we study detection rules which benefit from results obtained in image processing. For the sigma-filter studied there to detect edges, asymptotic bounds for the normed delay have been established for independent data. These results are considerably extended in two directions. First, we allow for dependent processes satisfying acertain conditional mixing property. Second, we allow for more general pilot estimators, e.g., the median, resulting in better detection properties. Asimulation study indicates that our new procedure indeed performs much more better.

Statistics & Decisions, Oldenbourg Wissenschaftsverlag

Print ISSN: 0721-2631
Volume: 21, 04/2003
Pages: 343

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