Multiple Change Point Detection in Time Series with Nonstationary Dynamics

Change point detection (CPD) identifies points within data sequences where statistical properties undergo significant changes, playing a vital role in domains such as finance, climate science, and quality control. Traditional CPD algorithms often assume piecewise stationarity, where model parameters remain constant between consecutive change points. However, this assumption is frequently violated in real-world data, which commonly exhibit continuous nonstationary dynamics. Such dynamics can obscure abrupt changes or lead to false detections, complicating the detection process. To address these challenges, we propose a model-based CPD algorithm capable of handling nonstationary dynamics while accounting for temporal and cross-correlations. The model decomposes time series into two components: a random walk to represent nonstationary dynamics and a vector autoregressive process to capture temporal and cross-correlations. Change points are identified by measuring error reduction within a moving window when abrupt changes are introduced into selected components of the time series. Key features of the algorithm include its flexibility to incorporate a broad range of component selection procedures that satisfy the sure screening property and parameter estimation techniques under mild conditions. The consistency of the change point estimator, including the number and locations of change points, is established for general choices. A specific implementation that employs l1-regularization for component selection and introduces a novel procedure for parameter estimation is proposed. This algorithm iteratively estimates model parameters, nonstationary dynamics, and multiple change point locations simultaneously. The algorithm’s effectiveness is demonstrated through applications to both simulated and real-world data. For instance, in images from the steel rolling process, the algorithm identifies surface defects amid gradual background variations. Similarly, in solar surface data, it detects solar flares against dynamic backgrounds. These applications highlight the algorithm’s robustness and versatility across diverse scenarios.