The detection and estimation of change-point(s) in the mean is a classical problem in statistics and has broad applications in a wide range of areas. Though many methods have been developed in the literature, most are applicable only under a specific dimensional setting. Specifically, the methods designed for low-dimensional problems may not work well in the high-dimensional environment and vice versa. Motivated by this limitation, we propose a dimension-agnostic procedure of change-point testing for time series by applying dimension reduction and self-normalization. Our test statistics can accommodate both temporal and cross-sectional dependence, and capture both sparse and dense changes, regardless of the dimensionality. An extension to change point estimation is also made via the wild binary segmentation. These appealing features are supported by both asymptotic theory and numerical studies.