Structural change detection in time series based on DP with action cost

Even if an appropriate prediction expression and/or model are constructed to fit a time series, the model gradually begins to fail the prediction of the time series from some time point. In such case, it would be important not only to quickly detect the failing situation but also to renew the prediction model after the detection as soon as possible. In this paper, we formulate the structural change detection in time series as an optimal stopping problem, using the concept of DP (dynamic programming). The cost function is defined as the sum of a loss cost by failing and an action cost after the detection. And we propose a method for optimal solution and show the correctness. Also we clarify the effectiveness by experimentations.