We submitted two systems to the SemEval-2016 Task 12: Clinical TempEval challenge, participating in Phase 1, where we identified text spans of time and event expressions in clinical notes and Phase 2, where we predicted a relation between an event and its parent document creation time. For temporal entity extraction, we find that a joint inference-based approach using structured prediction outperforms a vanilla recurrent neural network that incorporates word embeddings trained on a variety of large clinical document sets. For document creation time relations, we find that a combination of date canonicalization and distant supervision rules for predicting relations on both events and time expressions improves classification, though gains are limited, likely due to the small scale of training data.