An acceleration-based structural health monitoring approach for building structures under earthquake using ARX model and neural network (NN) model is proposed in this paper. The ARX and NN models were constructed using the healthy structure with moderate input. Then the prediction-error for other inputs is obtained to estimate the damage existence and its extent. In previous studies the prediction error is usually used to measure the damage level by comparing the amplitude of the error. In this study, the analysis of dynamics of prediction-error is proposed to improve the accuracy of the damage identification. The approach is further improved by using the acceleration at later time steps. The delay of time was considered as a tunable band corresponding to different structures. To facilitate using possibly less sensors, the acceleration streams at the same location but at different time steps were utilized. The prediction accuracy could be raised by the increment of number of acceleration streams at different time steps to an appropriate value. In our proposed evaluation approach, damage occurrence alarm could be obtained practically and economically only using readily available acceleration time histories. The method was applied to a full-scale two-storey wooden building tested at the E-Defense. At the final step, the shake table was excited to reproduce the ground acceleration of large earthquake obtained at Kobe. The building was destructed finally by this earthquake input In the course of the shake table tests, many levels of inputs were applied to the building to see its degradation by the shake. The method proposed here was applied to see its effectiveness and applicability. We will show that the dynamic characteristics of the prediction error have many important information on the degree of damage and the modes of the damage that would not be obtained just by looking at the amplitude of the error.