Two major issues in the specification of the thermospheric density are the definition of proper solar inputs and the empirical modeling of thermosphere response to solar and to geomagnetic forcings. This specification is crucial for the tracking of low Earth orbiting satellites. Here we address both issues by using 14 years of daily density measurements made by the Stella satellite at 813 km altitude and by carrying out a multiscale statistical analysis of various solar inputs. First, we find that the spectrally integrated solar emission between 26–34 nm offers the best overall performance in the density reconstruction. Second, we introduce linear parametric transfer function models to describe the dynamic response of the density to the solar and geomagnetic forcings. These transfer function models lead to a major error reduction and in addition open new perspectives in the physical interpretation of the thermospheric dynamics.