Statistics and Computing

, Volume 16, Issue 2, pp 177–192 | Cite as

Modified repeated median filters

  • T. Bernholt
  • R. FriedEmail author
  • U. Gather
  • I. Wegener


We discuss moving window techniques for fast extraction of a signal composed of monotonic trends and abrupt shifts from a noisy time series with irrelevant spikes. Running medians remove spikes and preserve shifts, but they deteriorate in trend periods. Modified trimmed mean filters use a robust scale estimate such as the median absolute deviation about the median (MAD) to select an adaptive amount of trimming. Application of robust regression, particularly of the repeated median, has been suggested for improving upon the median in trend periods. We combine these ideas and construct modified filters based on the repeated median offering better shift preservation. All these filters are compared w.r.t. fundamental analytical properties and in basic data situations. An algorithm for the update of the MAD running in time O(log n) for window width n is presented as well.


Signal extraction Robust filtering Drifts Jumps Outliers Computational geometry Update algorithm 


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Copyright information

© Springer Science + Business Media, LLC 2006

Authors and Affiliations

  1. 1.Department of Computer ScienceUniversity of DortmundDortmundGermany
  2. 2.Department of StatisticsUniversity Carlos III de MadridGetafeSpain
  3. 3.Department of StatisticsUniversity of DortmundDortmundGermany

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