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Rumour stance classification, defined as classifying the stance of specific social media posts into one of supporting, denying, querying or commenting on an earlier post, is becoming of increasing interest to researchers. While most previous work has focused on using individual tweets as classifier inputs, here we report on the performance of sequential classifiers that exploit the discourse features inherent in social media interactions or ‘conversational threads’. Testing the effectiveness of four sequential classifiers – Hawkes Processes, Linear-Chain Conditional Random Fields (Linear CRF), Tree-Structured Conditional Random Fields (Tree CRF) and Long Short Term Memory networks (LSTM) – on eight datasets associated with breaking news stories, and looking at different types of local and contextual features, our work sheds new light on the development of accurate stance classifiers. We show that sequential …