Digitalizing real-world analog signals typically involves sampling in time and discretizing in amplitude. Subsequent signal reconstructions inevitably incur an error that depends on the amplitude resolution and the temporal density of the acquired samples. From an implementation viewpoint, consistent signal reconstruction methods have proven a profitable error-rate decay as the sampling rate increases. Despite that, these results are obtained under offline settings. Therefore, a research gap exists regarding methods for consistent signal reconstruction from data streams. Solving this problem is of great importance because such methods could run at a lower computational cost than the existing offline ones or be used under real-time requirements without losing the benefits of ensuring consistency. In this paper, we formalize for the first time the concept of consistent signal reconstruction from streaming time-series data. Then, we present a signal reconstruction method able to enforce consistency and also exploit the spatiotemporal dependencies of streaming multivariate time-series data to further reduce the signal reconstruction error. Our experiments show that our proposed method achieves a favorable error-rate decay with the sampling rate compared to a similar but non-consistent reconstruction.