Inferring from the occurrence pattern of slow slip events (SSEs) the probability of triggering a damaging earthquake within the nearby velocity weakening portion of the plate interface is critical for hazard mitigation. Although robust methods exist to detect long-term SSEs consistently and efficiently, detecting short-term SSEs remains a challenge. In this study, we propose a novel statistical approach, called singular spectrum analysis isolate-detect (SSAID), for automatically estimating the start and end times of short-term SSEs in GPS data. The method recasts the problem of detecting SSEs as that of detecting change-points in a piecewise signal. This is achieved by obscuring the deviation from piecewise-linearity in the underlying SSE signals using added noise. We verify its effectiveness on a range of model-generated synthetic SSE data with different noise levels, and demonstrate its superior performance compared to two existing methods. We illustrate its capability in detecting short-term SSEs in observed GPS data using 36 GPS stations in southwest Japan via the co-occurrence of non-volcanic tremors, hypothesis tests and fault estimation.