Many observational records critically rely on our ability to merge different (and not necessarily overlapping) observations into a single composite. We provide a novel and fully-traceable approach for doing so, which relies on a multi-scale maximum likelihood estimator. This approach overcomes the problem of data gaps in a natural way and uses data-driven estimates of the uncertainties. We apply it to the total solar irradiance (TSI) composite, which is currently being revised and is critical to our understanding of solar radiative forcing. While the final composite is pending decisions on what corrections to apply to the original observations, we find that the new composite is in closest agreement with the PMOD composite and the NRLTSI2 model. In addition, we evaluate long-term uncertainties in the TSI, which reveal a 1/f scaling
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