Data-adaptive structural change-point detection via isolation

In this paper, a new data-adaptive method, called DAIS (Data Adaptive
ISolation), is introduced for the estimation of the number and the location of
change-points in a given data sequence. The proposed method can detect changes
in various different signal structures; we focus on the examples of
piecewise-constant and continuous, piecewise-linear signals. The novelty of the
proposed algorithm comes from the data-adaptive nature of the methodology. At
each step, and for the data under consideration, we search for the most
prominent change-point in a targeted neighborhood of the data sequence that
contains this change-point with high probability. Using a suitably chosen
contrast function, the change-point will then get detected after being isolated
in an interval. The isolation feature enhances estimation accuracy, while the
data-adaptive nature of DAIS is advantageous regarding, mainly, computational
complexity. The methodology can be applied to both univariate and multivariate
signals. The simulation results presented indicate that DAIS is at least as
accurate as state-of-the-art competitors and in many cases significantly less
computationally expensive.