Predictive process monitoring (PPM) techniques utilize existing event logs to predict certain key metrics in running business processes. In terms of feature extraction, current PPM methods presuppose that cases are solely influenced by their attributes or exclusively encoded by extracting resource-level inter-case behavioral attributes. These methods typically overlook inter-case behavioral information from the activity perspective. This study proposes a new method to capture the inter-activity behaviour of cases (IABC), which involves a feature construction framework covering three dimensions: time window, activity granularity, and behaviour state. It constructs a total of 36 types of inter-activity behavioral features. Concurrently, this study proposes two novel algorithms: the influence distribution algorithm for mining positive/negative influence propagation among activities, and the batch behaviour detection algorithm for identifying potential batch operations. The effectiveness of the IABC method is evaluated on three publicly available event logs. The results demonstrate that the temporal prediction model integrating the IABC method outperforms both the baseline model, which does not use the method, and the model that employs resource-level inter-case features.