Sensor devices and embedded processors are becoming ubiquitous. Their limited resources (CPU, memory and/or communication bandwidth and power) pose some interesting challenges. We need both powerful and concise "languages" to represent the important features of the data, which can (a) adapt and handle arbitrary periodic components, including bursts, and (b) require little memory and a single pass over the data. We propose AWSOM (Arbitrary Window Stream mOdeling Method), which allows sensors in remote or hostile environments to efficiently and effectively discover interesting patterns and trends. This can be done automatically, i.e., with no user intervention and expert tuning before or during data gathering. Our algorithms require limited resources and can thus be incorporated in sensors, possibly alongside a distributed query processing engine [9, 5, 22]. Updates are performed in constant time, using logarithmic space. Existing, state of the art forecasting methods (SARIMA, GARCH, etc) fall short on one or more of these requirements. To the best of our knowledge, AWSOM is the first method that has all the above characteristics. Experiments on real and synthetic datasets demonstrate that AWSOM discovers meaningful patterns over long time periods. Thus, the patterns can also be used to make long-range forecasts, which are notoriously difficult to perform. In fact, AWSOM outperforms manually set up auto-regressive models, both in terms of long-term pattern detection and modeling, as well as by at least 10× in resource consumption.