Adaptive Change Point Inference for High Dimensional Time Series with Temporal Dependence

This paper investigates change point inference in high-dimensional time series. We begin by introducing a max-$L_2$-norm based test procedure, which demonstrates strong performance under dense alternatives. We then establish the asymptotic independence between our proposed statistic and the two max-$L_\infty$-based statistics introduced by Wang and Feng (2023). Building on this result, we develop an adaptive inference approach by applying the Cauchy combination method to integrate these tests. This combined procedure exhibits robust performance across varying levels of sparsity. Extensive simulation studies and real data analysis further confirm the superior effectiveness of our proposed methods in the high-dimensional setting.