In this paper, we investigate how the prediction paradigm from machine learning and Natural Language Processing (NLP) can be put to use in computational historical linguistics. We propose word prediction as an intermediate task, where the forms of unseen words in some target language are predicted from the forms of the corresponding words in a source language. Word prediction allows us to develop algorithms for phylogenetic tree reconstruction, sound correspondence identification and cognate detection, in ways close to attested methods for linguistic reconstruction. We will discuss different factors, such as data representation and the choice of machine learning model, that have to be taken into account when applying prediction methods in historical linguistics. We present our own implementations and evaluate them on different tasks in historical linguistics.