Despite being a major public health problem, falls in the elderly cannot be detected efficiently yet. Many studies have used acceleration as the main input to discriminate between falls and activities of daily living (ADL). In recent years, there has been an increasing interest in using smartphones for fall detection. The most promising results have been obtained by supervised Machine Learning algorithms. However, a drawback of these approaches is that they rely on falls simulated by young or mature people, which might not represent every possible fall situation and might be different from older people's falls. Thus, we propose to tackle the problem of fall detection by applying a kind of novelty detection methods which rely only on true ADL. In this way, a fall is any abnormal movement with respect to ADL. A system based on these methods could easily adapt itself to new situations since new ADL could be recorded continuously and the system could be re-trained on the fly. The goal of this work is to explore the use of such novelty detectors by selecting one of them and by comparing it with a state-of-the-art traditional supervised method under different conditions. The data sets we have collected were recorded with smartphones. Ten volunteers simulated eight type of falls, whereas ADL were recorded while they carried the phone in their real life. Even though we have not collected data from the elderly, the data sets were suitable to check the adaptability of novelty detectors. They have been made publicly available to improve the reproducibility of our results. We have studied several novelty detection methods, selecting the nearest neighbour-based technique (NN) as the most suitable. Then, we have compared NN with the Support Vector Machine (SVM). In most situations a generic SVM outperformed an adapted NN.