A novel time series analysis is presented to locate damage sources in a mechanical system, which is running in various operational environments. The source of damage is located by solely analyzing the acceleration time histories recorded from a structure of interest. First, a data normalization procedure is proposed. This procedure selects a reference signal that is 'closest' to a newly obtained signal from an ensemble of signals recorded when the structure is undamaged. Second, a two-stage prediction model (combining auto-regressive (AR) and auto-regressive with exogenous inputs (ARX) techniques) is constructed from the selected reference signal. Then, the residual. error, which is the difference between the actual acceleration measurement for the new signal and the prediction obtained from the AR-ARX model developed from the reference signal, is defined as the damage-sensitive feature. This approach is based on the premise that if there were damage in the structure, the prediction model previously identified using the undamaged time history would not be able to reproduce the newly obtained time series measured from the damaged structure. Furthermore, the increase in residual errors would be maximized at the sensors instrumented near the actual damage locations. The applicability of this approach is demonstrated using acceleration time histories obtained from an eight degrees-of-freedom mass-spring system.