Early structural change detection as an optimal stopping problem: solution theorem and its proof using reduction to absurdity

Authors:
Hiromichi Kawano;Tetsuo Hattori;Katsunori Takeda;Tetsuya Izumi
Affiliations:
NTT Advanced Technology, Musashino, Tokyo, Japan 180-0006;Graduate School of Engineering, Kagawa University, Kagawa, Japan;Graduate School of Engineering, Kagawa University, Kagawa, Japan;Micro Technica Co., Tokyo, Japan
Venue:
Artificial Life and Robotics
Year:
2010

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Abstract

The change point detection (CPD) problem in a time series is when it is found that the structure of the data being generated has changed at some time and for some reason. We have formulated structural change detection in a time series as an optimal stopping problem using the concept of dynamic programming (DP), and we present the optimal solution and its correctness by numerical calculations. In this article, we present the solution theorem and its proof using reduction to absurdity.