Long-term temporal information is crucial for event-based perception tasks, as raw events only encode pixel brightness changes. Recent works show that when trained from scratch, recurrent models achieve better results than feedforward models in these tasks. However, when leveraging self-supervised pre-trained weights, feedforward models can outperform their recurrent counterparts. Current self-supervised learning (SSL) methods for event-based pre-training largely mimic RGB image-based approaches. They pre-train feedforward models on raw events within a short time interval, ignoring the temporal information of events. In this work, we introduce TESPEC, a self-supervised pre-training framework tailored for recurrent architectures. To unleash the power of recurrent models, TESPEC is the first method utilizing longer sequences of events in the pre-training stage. TESPEC employs the masked image modeling paradigm with a new reconstruction target. We design a novel method to accumulate events into pseudo grayscale videos containing high-level semantic information about the underlying scene, which is robust to sensor noise and reduces motion blur. Reconstructing this target thus requires the model to reason about long-term history of events. Extensive experiments demonstrate our state-of-the-art performance in downstream tasks, including object detection, semantic segmentation, and monocular depth estimation.