Abstract The Web is a constantly expanding global information space that includes disparate types of data and resources. Recent trends demonstrate the urgent need to manage the large amounts of data stream, especially in specific domains of application such as critical infrastructure systems, sensor networks, log file analysis, search engines and more recently, social networks. All of these applications involve large-scale data-intensive tasks, often subject to time constraints and space complexity. Algorithms, data management and data retrieval techniques must be able to process data stream, i.e., process data as it becomes available and provide an accurate response, based solely on the data stream that has already been provided. Data retrieval techniques often require traditional data storage and processing approach, i.e., all data must be available in the storage space in order to be processed. For instance, a widely used relevance measure is Term Frequency–Inverse Document Frequency (TF–IDF), which can evaluate how important a word is in a collection of documents and requires to a priori know the whole dataset. To address this problem, we propose an approximate version of the TF–IDF measure suitable to work on continuous data stream (such as the exchange of messages, tweets and sensor-based log files). The algorithm for the calculation of this measure makes two assumptions: a fast response is required, and memory is both limited and infinitely smaller than the size of the data stream. In addition, to face the great computational power required to process massive data stream, we present also a parallel implementation of the approximate TF–IDF calculation using Graphical Processing Units (GPUs). This implementation of the algorithm was tested on generated and real data stream and was able to capture the most frequent terms. Our results demonstrate that the approximate version of the TF–IDF measure performs at a level that is comparable to the solution of the precise TF–IDF measure.