Time-encoded signals, such as social network update logs and spiking traces in neuromorphic processors, are defined by multiple traces carrying information in the timing of events, or spikes. When time-encoded data is processed at a remote site with respect to the location in which it is produced, the occurrence of events needs to be encoded and transmitted in a timely fashion. The standard Address-Event Representation (AER) protocol for neuromorphic chips encodes the indices of the "spiking"traces in the payload of a packet produced at the same time the events are recorded. This implicitly encodes the events' timing in the timing of the packet (which is assumed to be correctly detected at the receiver). This paper investigates the potential bandwidth saving that can be obtained by carrying out variable-length compression of packets' payloads. Compression leverages both intra-trace and inter-trace correlations over time that are typical in applications such as social networks or neuromorphic computing. The approach is based on discrete-time Hawkes processes and entropy coding with conditional codebooks. Results from an experiment based on a real-world retweet dataset are also provided.