Jump-Preserving Monitoring of Depending Time Series Using Pilot Estimators

Abstract

An important problem of the statistical analysis of time series is to detect change-points in the mean structure. Since this problem is a one-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. A simulation study indicates that our new procedure indeed performs much more better.

Cite this work

No public copy is stored for this record, so only the metadata is cited.

Stored only when both papers are in the corpus — 10 citations exist upstream.

Papers that cite the same references — the relational fallback while embeddings are still backfilling.