In this paper, we present a method for approximating the values of sensors in a wireless sensor network based on time series forecasting. More specifically, our approach relies on autoregressive models built at each sensor to predict local readings. Nodes transmit these local models to a sink node, which uses them to predict sensor values without directly communicating with sensors. When needed, nodes send information about outlier readings and model updates to the sink. We show that this approach can dramatically reduce the amount of communication required to monitor the readings of all sensors in a network, and demonstrate that our approach provides provably-correct, user-controllable error bounds on the predicted values of each sensor.