Structural Break Detection in Non-Stationary Network Vector Autoregression Models

Imagine a network, like a socialnetwork or a system of connected devices, is being observed over time. Each node in this network has certain measurements attached to it that can change, like the temperature of a device. Although the overall structure of the network remains constant, these measurements can vary, leading to a complex multivariate time series dataset that exhibits non-stationary characteristics over time. This paper applies a piecewise stationary network vector autoregressive (NAR) model to analyze these network data. The main idea is to partition the entire dataset into segments where the NAR model for each segment remains stationary. The identification of these segments, along with the determination of the NAR processes' autoregressive lag orders, are treated as unknowns. The minimum description length (MDL) principle is employed to develop a criterion for model selection that estimates these unknown parameters. A two-stage genetic algorithm is then formulated to tackle this optimization challenge. The MDL criterion is proven to be consistent in identifying the number and positions of the breakpoints - the junctures where adjacent NAR segments intersect. The effectiveness of the proposed method is demonstrated through simulation studies and real data analysis.