We are interested in capturing time series generated by small wireless electronic sensors. Battery-operated sensors must avoid heavy use of their wireless radio which is a key cause of energy dissipation. When many sensors transmit, the resources of the recipient of the data are taxed; hence, limiting communication will benefit the recipient as well. In our paper we show how time series generated by sensors can be captured and stored in a database system (archive). Sensors compress time series instead of sending them in raw form. We propose an optimal on-line algorithm for constructing a piecewise constant approximation (PCA) of a time series which guarantees that the compressed representation satisfies an error bound on the L_\infty distance. In addition to the capture task, we often want to estimate the values of a time series ahead of time, e.g., to answer real-time queries. To acheive this, sensors may fit predictive models on observed data, sending parameters of these models to the archive. We exploit the interplay between prediction and compression in a unified framework that avoids duplicating effort and leads to reduced communication.