Monitoring consists in deciding a log meets a given specification. In this work, we propose an automata-based formalism to monitor logs in the form of actions associated with time stamps and arbitrarily data values over infinite domains. Our formalism uses both timing parameters and data parameters, and is able to output answers symbolic in these parameters and in the log segments where the property is satisfied or violated. We implemented our approach in an ad-hoc prototype, and experiments show that its high expressive power still allows for efficient online monitoring.