Secure vehicular communication is a critical factor for secure traffic management. Effective security in intelligent transportation systems (ITS) requires effective and timely intrusion detection systems (IDS). In this paper, we consider false data injection attacks and distributed denial-of-service (DDoS) attacks, especially the stealthy DDoS attacks, targeting the integrity and availability, respectively, in vehicular ad-hoc networks (VANET). Novel statistical intrusion detection and mitigation techniques based on centralized communications through roadside units (RSU) are proposed for the considered attacks. The performance of the proposed methods are evaluated using a traffic simulator and a real traffic dataset. Comparisons with the state-of-the-art solutions clearly demonstrate the superior performance of the proposed methods in terms of quick and accurate detection and localization of cyberattacks.