Positive and unlabelled (PU) learning for multi-variate time series classification refers to build a binary classification model when only a small set of positive and a large set of unlabelled samples are accessible at training stage. Different from binary semi-supervised scenario in which the training set contains labelled samples from both positive and negative classes, in the PU learning setting, only positive samples are labelled due to cost-restriction or issues related to defining what belongs to the negative class. With the objective to deal with this challenging task, here, we propose a new deep learning framework, referred as DMTS-PUL. Our method has two different steps: firstly, it selects a set of reliable negative samples from the set of unlabelled data and, successively, it iteratively enriches the training data by selecting pseudo-labels to train a binary classification model via self-training. Experimental evaluations on several benchmarks have highlighted the quality of DMTS-PUL w.r.t. competing approaches and the obtained findings have pointed out the suitability of our proposal when only small amounts of positive labelled samples are available. INDEX TERMS Positive unlabeled learning, multi-variate time series, self-training, recurrent neural network.