Stress has become an important health problem, but existing stress detectors are inconvenient in long-term real-life use because users either have to wear dedicated devices or expend notable interaction efforts in system adaptation to specifics of each person. Adaptation is necessary because individuals significantly differ in their perception of stress and stress responses, but typical adaptation employs supervised learning methods and hence requires fairly large sets of labelled data (i.e. information on whether each reporting period was stressful or not) from every user. To address these problems, we propose a novel unsupervised stress detector, based on using a smartphone as the only device and using discrete hidden Markov models (HMM) with maximum posterior marginal (MPM) decisions for analysis of phone data. Our detector requires neither additional hardware nor data labelling and hence is truly unobtrusive and suitable for lifelong use. Its accuracy was evaluated using two real-life datasets: in the first case, adaptation was based on very short (a few days) phone interaction histories of each individual, and in the second case-on longer histories. In these tests, the proposed HMM-MPM achieved 59 and 70% accuracies, respectively, which is comparable with results of fully supervised methods, reported by other works.