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

Abstract

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.