BIT Numerical Mathematics

, Volume 54, Issue 4, pp 1155–1169 | Cite as

An algorithm for continuous piecewise linear bounding of discrete time series data

  • Andrew Skelton
  • Allan R. Willms


An algorithm for enclosing a given set of time series data inside a continuous piecewise linear band of varying height subject to certain constraints is presented. The band is defined by two piecewise linear curves that lie above and below the data respectively. Segments of these curves are constrained to start and end at one of the data points, and those whose slope does not lie between its neighbors’ slopes are required to be at least as wide as a user-specified value. The algorithm yields a band which accurately preserves the general trends of the data, while enclosing the inherent measurement noise. This band is typically obtained in \(O(n\log K)\) time, where \(n\) is the number of data points and \(K\) is the number of linear segments. The algorithm is described and its capabilities are tested on four data sets. Comparisons are made with alternative algorithms.


Continuous representation Piecewise linear representation  Time series Algorithm Parameter estimation 

Mathematics Subject Classification (2010)

65D10 65G40 


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Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  1. 1.University of GuelphGuelphCanada

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