B1158
Title: Adaptive MOSUM: Inference for change points in high-dimensional time series
Authors: Likai Chen - Washington University in Saint Louis (United States) [presenting]
Michel Ferreira Cardia Haddad - Queen Mary University of London (United Kingdom)
Jiaqi Li - University of Chicago (United States)
Hangcen Zou - Washington University in Saint Louis (United States)
Abstract: Moving sum (MOSUM) test statistic is popular for multiple change-point detection due to its simplicity of implementation and effective control of the significance level for multiple testing. However, its performance heavily relies on selecting the bandwidth parameter for the window size, which is extremely difficult to determine in advance. To address this issue, an adaptive MOSUM method is proposed, applicable in both multiple and high-dimensional time series models. Specifically, an $\ell^2$-norm is adopted to aggregate MOSUM statistics cross-sectionally and take the maximum over time and bandwidth candidates. The asymptotic distribution of the test statistics is provided, accommodating general weak temporal and cross-sectional dependence. By employing a screening procedure, the number of change points can be consistently estimated, and the convergence rates for the estimated timestamps and sizes of the breaks are presented. The asymptotic properties and the estimation precision are demonstrated by extensive simulation studies. Furthermore, an application is presented using real-world COVID-19 data from Brazil, wherein the distinct outbreak stages are observed among subjects of different age groups and geographic locations. These findings facilitate the analysis of epidemics, pandemics, and data from various fields of knowledge exhibiting similar patterns.
