  Sagittarius A* (Sgr A*) is the variable radio, near-infrared (NIR), and X-ray
source associated with accretion onto the Galactic center black hole. We
present an analysis of the most comprehensive NIR variability dataset of Sgr A*
to date: eight 24-hour epochs of continuous monitoring of Sgr A* at 4.5 $\mu$m
with the IRAC instrument on the Spitzer Space Telescope, 93 epochs of 2.18
$\mu$m data from Naos Conica at the Very Large Telescope, and 30 epochs of 2.12
$\mu$m data from the NIRC2 camera at the Keck Observatory, in total 94,929
measurements. A new approximate Bayesian computation method for fitting the
first-order structure function extracts information beyond current Fast Fourier
Transformation (FFT) methods of power spectral density (PSD) estimation. With a
combined fit of the data of all three observatories, the characteristic
coherence timescale of Sgr A* is $\tau_{b} = 243^{+82}_{-57}$ minutes ($90\%$
credible interval). The PSD has no detectable features on timescales down to
8.5 minutes ($95\%$ credible level), which is the ISCO orbital frequency for a
dimensionless spin parameter $a = 0.92$. One light curve measured
simultaneously at 2.12 and 4.5 $\mu$m during a low flux-density phase gave a
spectral index $\alpha_s = 1.6 \pm 0.1$ ($F_\nu \propto \nu^{-\alpha_s}$). This
value implies that the Sgr A* NIR color becomes bluer during higher
flux-density phases. The probability densities of flux densities of the
combined datasets are best fit by log-normal distributions. Based on these
distributions, the Sgr A* spectral energy distribution is consistent with
synchrotron radiation from a non-thermal electron population from below 20 GHz
through the NIR.
