Adaptive Two-Way MOSUM

Music City Center 

The 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 the selection of the bandwidth parameter for the window size, which is extremely difficult to determine in advance. To address this issue, we propose an adaptive MOSUM method, applicable in both multiple and high-dimensional time series models. Specifically, we adopt an $\ell^2$-norm to aggregate MOSUM statistics cross-sectionally, and take the maximum over time and bandwidth candidates. We provide the asymptotic distribution of the test statistics, accommodating general weak temporal and cross-sectional dependence. By employing a screening procedure, we can consistently estimate the number of change points, 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, we present an application using real-world COVID-19 data from Brazil, wherein we observe distinct outbreak stages among subjects of different age groups and geographic locations.

multiple change-point detection, ℓ2 inference for break existence, Two-Way MOSUM, Gaussian approximation, temporal and spatial dependence, nonlinear time series