Novel method for structural change detection in time series using DP with an action cost

Even if an appropriate prediction expression and/or model is constructed to fit a time series, the model gradually begins to fail the prediction of the time series from some time point. In such a case, it is important not only to detect the failing situation quickly, but also to renew the prediction model as soon as possible after the detection. We formulate the structural change detection in a 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. We propose a method for optimal solution and show the correctness. Also, we clarify the effectiveness by a numerical experiment.