  Identifying change points (CPs) in a time series is crucial to guide better
decision making across various fields like finance and healthcare and
facilitating timely responses to potential risks or opportunities. Existing
Change Point Detection (CPD) methods have a limitation in tracking changes in
the joint distribution of multidimensional features. In addition, they fail to
generalize effectively within the same time series as different types of CPs
may require different detection methods. As the volume of multidimensional time
series continues to grow, capturing various types of complex CPs such as
changes in the correlation structure of the time-series features has become
essential. To overcome the limitations of existing methods, we propose TiVaCPD,
an approach that uses a Time-Varying Graphical Lasso (TVGL) to identify changes
in correlation patterns between multidimensional features over time, and
combines that with an aggregate Kernel Maximum Mean Discrepancy (MMD) test to
identify changes in the underlying statistical distributions of dynamic time
windows with varying length. The MMD and TVGL scores are combined using a novel
ensemble method based on similarity measures leveraging the power of both
statistical tests. We evaluate the performance of TiVaCPD in identifying and
characterizing various types of CPs and show that our method outperforms
current state-of-the-art methods in real-world CPD datasets. We further
demonstrate that TiVaCPD scores characterize the type of CPs and facilitate
interpretation of change dynamics, offering insights into real-life
applications.
