Time-series processing is a major challenge in machine learning with enormous progress in the last years in tasks such as speech recognition and chaotic series prediction. A promising avenue for sequential data analysis is quantum machine learning, with computational models like quantum neural networks and reservoir computing. An open question is how to efficiently include quantum measurement in realistic protocols while retaining the needed processing memory and preserving the quantum advantage offered by large Hilbert spaces. In this work, we propose different measurement protocols and assess their efficiency in terms of resources, through theoretical predictions and numerical analysis. We show that it is possible to exploit the quantumness of the reservoir and to obtain ideal performance both for memory and forecasting tasks with two successful measurement protocols. One repeats part of the experiment after each projective measurement while the other employs weak measurements operating online at the trade-off where information can be extracted accurately and without hindering the needed memory. Our work establishes the conditions for efficient time-series processing paving the way to its implementation in quantum devices.