Fault detection is indispensable for preserving both the safety and efficiency of the air handling unit (AHU) system. However, the AHU system not only shows time-varying dynamics but also poses difficulties in obtaining fault data. The existing fault detection methods seldom consider the above two problems at the same time, which leads to the reduction of fault detection accuracy. In response to these challenges, we present CA-FAOCC, a novel approach for fault detection that merges cointegration analysis (CA) and a fault-oriented adversarial one-class classifier (FAOCC). First, the feature extraction of the AHU system is carried out by CA to handle its time-varying dynamic characteristics. Next, considering the common issue of limited fault samples in real-world environments, FAOCC transforms the fault detection problem into a one-class classification problem. Only the features derived from the system's normal operation data are used for training, and the trained model is then applied to fault detection. Finally, experimental results based on the ASHRAE RP-1312 dataset demonstrate that the CA-FAOCC approach effectively overcomes the aforementioned challenges.