  The temporal and spatial spectral evolution of the jets of AGN can be studied
with multi-frequency, multi-epoch VLBI observations. The combination of both,
morphological and spectral parameters can be used to derive source intrinsic
physical properties such as the magnetic field and the non-thermal particle
density. In the first two papers of this series, we analyzed the single-dish
light curves and the VLBI kinematics of the blazar CTA 102 and suggested a
shock-shock interaction between a traveling and a standing shock wave as a
possible scenario to explain the observed evolution of the component associated
to the 2006 flare. In this paper we investigate the core-shift and spectral
evolution to test our hypothesis of a shock-shock interaction. We used 8
multi-frequency VLBA observations to analyze the temporal and spatial evolution
of the spectral parameters during the flare. We observed CTA 102 between May
2005 and April 2007 using the VLBA at six different frequencies spanning from 2
- 86 GHz. After the calibrated VLBA images were corrected for opacity, we
performed a detailed spectral analysis. From the derived values we estimated
the magnetic field and the density of the relativistic particles. The detailed
analysis of the opacity shift reveals that the position of the jet core is
proportional to nu^-1 with some temporal variations. The value suggests
possible equipartition between magnetic field energy and particle kinetic
energy densities at the most compact regions. From the variation of the
physical parameters we deduced that the 2006 flare in CTA 102 is connected to
the ejection of a new traveling feature (t=2005.9) and the interaction between
this shock wave and a stationary structure around 0.1 mas from the core. The
source kinematics together with the spectral and structural variations can be
described by helical motions in an over-pressured jet.
