Detecting structural changes in dependent data

In the era of big data, a frequently encountered task is to model and identify structural changes in the data generating process. It is quite challenging especially when data are dependent and massive, requiring computationally efficient analysis. To address the challenge, we model the data generating process as a segment-wise autoregression, and propose a multi-window method that is both effective and efficient for discovering the structural changes. The proposed approach was motivated by transforming a segment-wise autoregression into a multivariate time series that is asymptotically segment-wise independent and identically distributed. We then derive theoretical guarantees for (almost surely) selecting the true number of change points of segment-wise independent multivariate time series. In particular, we prove that a wide variety of penalized selection procedure produces a strongly consistent selection of the optimal number of change points, under mild assumptions. We demonstrate the theory and strength of the proposed algorithms by experiments on both synthetic and real-world data.