Smart home devices are vulnerable to passive inference attacks based on network traffic, even in the presence of encryption. In this paper, we present PINGPONG, a tool that can automatically extract packet-level signatures for device events (e.g., light bulb turning ON/OFF) from network traffic. We evaluated PINGPONG on popular smart home devices ranging from smart plugs and thermostats to cameras, voice-activated devices, and smart TVs. We were able to: (1) automatically extract previously unknown signatures that consist of simple sequences of packet lengths and directions; (2) use those signatures to detect the devices or specific events with an average recall of more than 97%; (3) show that the signatures are unique among hundreds of millions of packets of real world network traffic; (4) show that our methodology is also applicable to publicly available datasets; and (5) demonstrate its robustness in different settings: events triggered by local and remote smartphones, as well as by homeautomation systems.