We introduce DocTime - a novel temporal dependency graph (TDG) parser that takes as input a text document and produces a temporal dependency graph. It outperforms previous BERT-based solutions by a relative 4-8% on three datasets from modeling the problem as a graph network with path-prediction loss to incorporate longer range dependencies. This work also demonstrates how the TDG graph can be used to improve the downstream tasks of temporal questions answering and NLI by a relative 4-10% with a new framework that incorporates the temporal dependency graph into the self-attention layer of Transformer models (Time-transformer). Finally, we develop and evaluate on a new temporal dependency graph dataset for the domain of contractual documents, which has not been previously explored in this setting.